Going on everyone Sam here with late sports cards. We're been 22 23. I need contenders basketball 12 box case break number 11 tiered random team style There's a look again at your random results as always you can find those on the website under the results tab as well as the Lincoln Chat Let's do everybody. Good luck here Yeah, yeah, Admiral they so forest and Lane and rich took the the main streaming setup Boca Raton for the SGC Grading event tomorrow, so I'm over in Matt's Matt's studio today. I Got thrown to the side Tenders really bro who overhead empty case Imagine that happen. That'd be bad. Yeah, good luck here, everybody Good lord, dude print rookie with a second owner of the game in the third inning good lord. There's a final stick at Tyrese Halliburton to 49 Oh Jalen Williams rookie the your contenders first auto is Frank selvi st. Louis Hawks will go to Atlanta to 199 When he was listed is out Where are the robots have taken over the Navy? Not the Navy Chris Paul to 249 I If this guy is making this guy is making fun of me Hitting V and not hitting and not copycasing. He's getting kicked out There's Steph Curry. You did it Yeah, see Poster results. There's just a beat. There was like BVB. Wait, really? Yeah That's your Malachi brand I'm there shade on sharp rookie ticket auto nice one there great movie by the way for us one My favorites of all time nice one there That's blazers blazes out of here What I look like I'm sort of cool to you You're getting aggressive. Oh, yeah, we're just launching packs left and right now Sadiq Bay to 99 semi-final stick it In IV rookie of the year contender sweet shot Shaquille O'Neal Shet Saw there's a Galvin Johnson 42 of 99 for the spurs nice one there that spurs that chat rookie out of there, too This guy's just and not handle top loaders. No, it's slippery. There's a John and Kaminga to 249 shade all that popcorn base That's probably in sports. Honestly Chris sale versus throwback jerseys Cracked ice Cade Cunningham six of 25 sweet shots I don't know why it's funny Benedict, Matherin And That is Alfred Shenyoon one of ten on the sophomore contender's auto nice one there for the Rockets Turkish Tim Duncan turd Duncan I can dobson beer Did my buddy said anything else? It's like the bucks without Yannis or an 18 I said do they stink and he goes generally if you take the best player off a team They aren't very good Not true. I'm just gonna I'm just gonna just gonna instigate About sure a young or good That There's Lonzo ball to you to 49 lottery ticket chef sweet shots Jordan pool. Oh, you said it with more Like a higher higher fish Yeah, I am doing personal tonight's act. Yes, sir. I'm so No, sir LeBron legendary contenders Willie Anderson for the spurs 2199 no, sir There's still one 99 Gordon a little Melville Give the whole Carmelo Benedict Matherin Jaden Ivy one of 49 Poison Ivy going to the Pistons Ryan S. Congrats, buddy I thought you're about to say 101 again Now now one of 49 Jaden Ivy finals take it. We'll get that mag. It's a submarine. What's very nice You like there's gonna be a one-on-one here. I do I feel it Feel it in my blood Luca throwback Ochaic Baji premium that yonte Murray That you're gonna say one of one, too WWE main event Throwback jerseys Worcester TV's Gatorade coolers for sale the picture on the Pobachi on the Red Docks, it's just that case. Yeah, I've always seen that case, dude Sweet shot stunk in Robinson Barry Smith Trevor Kiehl's Variation premium rookie ticket order. There's Cole Anthony 2199 a lottery ticket shade on a sharp Viren on the left Oh, that's why Andrew Nemhardt variation Nice and Daniels Grant Hill legendary contenders for the pistons 49 48 of 49 distance Gee money. Yeah, you put the order in now if you want Zach. Yeah, you'll be second in queue You'll be second in queue Mike Conley to 249 Nicholas T Assorted stuff, what is it? Uh Dynasty Bowman Jumbo and then six archives. How does it feel that Franchi Cordero? It's like the next Babe Ruth on the Yankees Pobachi boom Do it right now, you guys you have my trash, okay, bam out of bio to 249.  There's like a billion cards in this That's a nice one though cracked ice to 25 Steph Curry on the sweet shots There's a Tim Hardaway to 199 Shade on sharp to 99. There we go. Congrats on that Blazers 11 of 99 and this should just be like four base cards You can make that sure That was a hot pack right there unintentional hot pack Pobachi bang nothing but freakin bag dude Sam's They are Jabari Walker nice one there for the Blazers, no, I did not Vaughn What was what was it? Do you like inscribe it something funny like Jalen Suggs dude Jalen Suggs inscribed in eminence Like his one-of-one RPA says I sweated in this That's Peyton Watson. He's so funny Sohan base base Play a king of the court now to 11 There's Anthony Davis to 249 Keegan Murray sweet shot Jalen Brown We can record it some time There's a semi-final stick a Tyler hero to 99 Yeah, I like this train if you want to see I'm showing him Pobachi Hey Yeah, Leraavia's inscriptions are sweet dude that one Leraavia out of elite was so cool Zachal mean 249 The beard more high and tight It must be honestly must look that way at least The beard has not really been taken care of over the past week beard needs to be taken care of a little bit better I say I'm oblique nice one there for the Cavaliers There's Mark Williams rookie ticket auto For anyone besides me Base and base 275 Kade Cunningham Conference finals ticket. It's the camera angle. Yeah, true. It must be the camera angle. That's true, too. It's a good point actually Premium rookie ticket auto Keegan Murray is Jake Leraavia nice one there for the Grizzlies Not the Navy Keep coming back Not the Navy Good ride the robots taking over the Navy Pobachi over Donnie bang, baby. Let's go get Mike Breen in the air Still went in though still went in There's Lonzo ball to 99 Donnie was so mad that that just went in. I don't really care.  That's how mad he is Hey cartoon character That's is that Carl Anthony Towns to 249 a lot of a ticket shade on sharp. There's David Roddy Nice one there for the Grizzlies on the variation See thing is right. There's osmane zheng variation rookie ticket for the Thunder superstar Trey young that is a License to dominate super short print going to the Rockets Jalen Green nice one there. You just Redemption Peyton Watson rookie season ticket going to the Nuggets nice one there Denver Peyton Watson Yes, I still got that That pick it though. I still got that pick it I pulled Rory pick it because Kyle pulled the one-on-one for Rory and he's tied with me now I think it was in there last year to be honest Rory the license to dominate There's cam Thomas to 49 base Classic clip. Oh, yeah big-time classic clip Variation Deontay Murray recently suspended Deontay Murray He can Murray that is very eason nice one there for the Rockets base take it out Yeah, I was gonna say I do remember brief like vaguely that being in it last year Desmond Bain to 199 first round ticket. Yeah, it is cool. So good. It's a good design for sure That is Ryan Rollins variation rookie ticket on for the Warriors Base base Yeah, exactly. It's like the passports and prestige very true very true Hibachi and that's in close but it went in ugly, but it worked Same five-footers or not Deontay Murray another variation that is Permit to dominate Christian Brown nice one there for the nuggets Super short print as well usually get one license one permit, which is good one rookie one fat base that's EJ Liddell On the rookie ticket variation nice one there for the pelicans base and base Yeah You are right you would win that bet that is Evan Mobley to 249 for the cap Russell Westbrook Take it to the hall. We've got Steph Curry first round to get a 199 for the Warriors Dyson Daniels Max Christie nice one there for the Lakers rookie ticket base auto Max Christie Once that guys to the go. There's a Zach Levine to 199 for the Bulls so on lottery ticket Base boss a we got a cracked ice It is Kennedy Chandler 10 of 25 nice one Memphis on the cracked ice rookie ticket audit Grads on that their Memphis space base Gordon Hayward to 249 base Premium auto their CJ McCollum variation Hegan Mary that is Mark Williams variation a rookie ticket premium auto the Hornets Demontus Sabonis Oh We're still rocking it Jason. You know it Another rookie ticket or just a premium ticket coming up. Moussa Diabata for the Clippers Variation That's gonna be Jalen Durin. There you go. Pistons nice one there on the premium rookie ticket auto on Hard elf bolts to 199 for the magic do to go old jolly make some time up on contenders. Oh another cracked ice Hello rookie. Is that a sign? Is it gonna be a pillow cracked ice? Sick Wendelmore, Jr. Three of 25 nice one there for the Timberwolves and Say my thing for what? Oh, how you doing Jalen? How you doing? Bear true Very true, and I got a I got to think quick for Wednesday too because bowman's usually like Great for funny stuff to 75 is dairy grown. I'll get it on Saturday then still a quick recap here guys I know you won't them off Saturday That's Christian Brown Jalen Green Wendelmore cracked ice Jalen Durin Mark Williams cracked ice Kennedy Chandler Max Christie E. J. Liddell Ryan Rollins Terry Eason Peyton Watson David Roddy jakeler avia Mark Williams Jabari Walker Billy Knight Grant Hill Trevor Keels Willie Anderson Alfred Shengun Keldon Johnson shade on sharp Frank selvi There's shade on sharp to 99 and Jalen or Jaden ivy to 49 very nice. That'll do it for the break guys Thanks again for the fill next up. We're on the football


If you are a first-time property buyer or you're just in the market for your next investment, you might be in search of some guidance and where better to get this from other than South Africa's Premier Property Expo, brought to you exclusively by Private Property. Now the Property Buyer show brings all industry professionals together, skilled to handle any question you might have and to guide you expertly through the process of buying your first home. And here to tell us everything we need to know about the show is Private Property's event manager of the Property Buyer show, Benjamin Jones. Thank you very much. Benjamin, welcome to the show. Thank you. So the Property Buyer show is basically in my mind that one-stop shop for anyone who's interested in buying or investing in property. But for those who have not experienced the Expo before, tell us exactly what it entails. Sure, so the Expo entails two theatres that we have basically educating your first-time buyers as well as your property investors, your more experienced and aspiring property investors. The first-time buyer content is really aimed at getting your home loan, getting your credit checked, taking out your first home loan and getting your finances in order. And then obviously your investor side of things is more about tax benefits as well as where to look for hotspots, investment hotspots for property. So as a visitor, you can come through and really get your questions answered and leave with informed decisions on your future and in your property journey. Private Property has been the proud sponsor of this event since 2017, but I also heard that there's very exciting news that you now own the show, which is amazing. What does this acquisition mean for the show itself and for the business? Sure, so everyone knows Private Property as a website, as a digital portal for finding property. The Private Property obviously acquired the property by a show and it really gives us that face-to-face engagement with our consumers or our property shoppers at the end of the day and really answer their questions in a live environment. It's always hard to kind of ask questions over the internet and try and get those answers where you can really speak to someone face-to-face, really get that professional advice and at the end of the day, it's not expensive. You know when I'm at these things, I always like to know that there's a young deal available every now and then. Is there any deal to look forward to at the expert? Of course, our exhibitors always have on-site specials, whether you're an investor or a first-time buyer. There's development launch prices, there's savings on deposits and then obviously there's free credit checks. As a first-time buyer, you have to have your credit in order to take out a home loan. So obviously some of our exhibitors are offering free credit checks and free consultations which you don't have to pay thousands of Rand per hour for. Amazing. Wow, that's fantastic. It seems like the property buyer shows basically checked all the boxes in. Hopefully. I think so. Well thank you. Thank you so much Benjamin for sharing this much needed information with us. I think you've set a lot of people's hearts at ease. Thank you. That's fantastic. The property buyer show takes place on the sixth and seventh of April at the Cape Town International Convention Center. If you're looking to purchase tickets, well you can head to www.propertybuyershow.com and for Durbin and Jo Berg don't feel left out because the show will be in Durbin from the 3rd to the 4th of August at Johannesburg from the 18th to the 20th of October. So you too can learn everything you need to know about buying property and for more information visit www.privateproperty.co.ca.


I'm loving I'm tipsy cuz I've been sipping on Hindi. I got the study of my vision and she ain't from the city She informed and she born a lot of way you twerk a shawty. What's up, everybody? I'm Miva Rabbit. We are here on Forza Motorsport 7. We do have the stock G920 rims still hooked up and We do have our 350z that we have still tuned from last episode here today to do a little bit of initiating without a handbrake handbrake initiations Mainly trying to drift on a handbrake because I know a lot of people don't have a external handbrake They're trying to find the button when it's spinning and it's really not that easy. I know I don't have a button here It's over here, but It's not as easy to find a button when the wheels rotating around like okay Where's this button? Where's this button looking away from the screen? So we're gonna do some drifting today without a handbrake and Basically kind of show that it is possible to use the way of the car and brakes to Drift without it. It helps a lot to have a handbrake, but if you don't have one You don't really necessarily need one Or weight transfers to get the car slotting so we can just kick it one way Let's kick the other way Use the clutch to stay sideways Cut the line a little bit because of lack of power We're on the way to the car Use that little left foot braking because we did lower the brake pressure down I believe either on this car or the other one actually the sink to this car has factory brakes Think of the 370. So we were able to do that without without a handbrake Is it easy once you get going not really It's really hard to do some turns without a handbrake because you're gonna have to really rely on your left foot braking to Make sure you slow yourself into the turn and not understeer like I did there Then you can get back Like that no handbrake needed Try to run this out Like right there. We're gonna have to really pop that clutch and really clutch kick that to Get that car slotting because it started understeer on us now quick handbrake pull will fix that so there is many different ways to do it We're gonna try and do kind of now. I guess a quicker entry and use brakes So there's many different ways that you can actually start it Do I recommend drifting on the handbrake now I can use the button. I would definitely use the button because This is Not the easiest thing to do And it has to be very well times in order for it to Really work really got to rely on left foot brakes and clutch kicks and just know the track and know the line because a Quick handbrake pull could adjust your line as well as brakes But when you're not using a handbrake and you just got to rely on Say the weight of the car like this You can run into the issue unless you tune your brakes to be more or biased where you will get understeer We're trying to do this without a handbrake If it's possible and it is You just got to use way more clutch and maybe a little bit of a grass line there. I think it's true self sideways, but it is Definitely possible to use the weight of the car a little mongee here Part of the brakes a little bit misjudged, but still got it sideways We're gonna just save that little grass line the left foot brake keep the car on the track And we're able to do that without a without a handbrake, so we're gonna try and do that first turn again Let's take this way And we started under so that's where I would have you know like to pull my e-brake and Definitely get the car going Brakes and clutch take to keep the car sideways So it is possible to put on a handbrake is an easy Not really But I recommend it you have to I prefer a little bit of a handbrake grab, but I am trying to do a lot more driving now without a handbrake We're gonna see if we can't Get this better Oh, that was really well That's a very impressive flick What hey it worked We're in line on the turn and the outside edge where I want to be at the front apron Strips Like it back oh boy So just think without a handbrake Definitely not easy, so we're gonna switch up tracks try it again at some other tracks Definitely not easy But it is possible So we are going to Find another track that could be fun Prog would be very hard Rio Atlanta There's a lot of these higher speed corners You would definitely need a handbrake to pitch the car into initiation from the straight line So I feel like we're gonna go try Mipple Valley see if we can't do this and Mipple Valley This might be a quite complicated in the first turn, but we're gonna give it a shot and see how it goes Not promising super super much, but We'll see what happens Once the track loads So I hope you guys are enjoying these tutorials definitely gonna be doing some more If you guys have ideas on something people like to see in a say a tutorial with the G920 or something like that Let me know down in the comments down below Maybe as technique Tandems and stuff like that are to come but like maybe a technique or something that you guys are Trying to get or practice on or what a challenge me to try let me know Because I'm always up for a challenge We're not gonna use a handbrake You know, I just grabbed it So I'm not sure how this car is gonna handle in this first turn Punch kick in there But kind of does Stretching that third gear out there. So when it comes to This track To be a lot of clutch kicks and a lot of left-foot brakes to keep weight, but she coming up here on this bridge We're gonna try and We're gonna try and definitely Get the car sideways through this whole section That's gonna work. I was a little bit too early So we definitely had to bail out on that one Which is something You got to learn how to do too You don't think you're gonna make the corner You do you could have to bail. I know it's not a real car. So you rack it's no big deal, but still Knowing when to bail out is a good thing as well this is actually a somewhat difficult But it is still fun sideways That grass life though grass roots. It's not what grass roots means, but hey, we'll break to flip it over On top of the brakes. I think we're good So not as bad as I thought this was gonna be Oh, so we wrecked well, good thing it's not a competition car So we're gonna give this a shot and try and do this a little bit faster wasn't too too bad of a Attempt there. We're gonna see if we can't do that under the bridge section again. Well, we're down for a minute They've adjust something on my screen that uh, totally popped up on me I felt like taking all those cones and that got really slippery. All right, so we're gonna see if we can do this Not sure how the speed is gonna work So that did not work out We had a little bit of a screen issue We've corrected that and we're still drifting without a handbrake doing everything That we can all the clutch kicks keep this car sideways The clutch kicks, trends and sparks, long clutch kicks. We are able to drift somewhat Now it's not as super flowy As if you have a handbrake as you can see we're gonna do the next lap with full handbrake Fritz because This is definitely not my normal drifting So we are gonna run this lap with handbrake full handbrake. We're gonna run it how we would Normally back first so much Here we go, we're gonna run this one how we would be at normal handbrake and everything Still only use the handbrake a little bit there. Oh boy That grass line though I don't think this car has the full amount of power to do this section of the track Now we that we have our handbrake and we are using it to see the difference not more slides So now I know we will definitely be able to get this under bridge section for sure Having the ability to use a handbrake there Definitely makes that whole section much easier to drive But I've noticed that I've been using the handbrake a lot less in certain sections of tracks now We're no longer pull the handbrake all the time. I'm using the weight so it is definitely possible so just a little bit of a Test for no handbrake in the beginning of this episode to see to show you guys a little bit of benefits of a handbrake and That is possible to do it without it We now look as cool. It could be a little bit harder but You don't need to use a handbrake as a clutch or as a crutch Because you do need a clutch Don't need a handbrake as a clutch to drive Because a lot of people rely a lot on it When we get more into tandoos and more into leading handbrakes will become more useful as well as hindrance as well Because you can do that and get greedy with it And if you were a drifting in Japan, they don't privy you can't brake So not a style I'm very much used to so that's why I was doing it say different practicing it and seeing how it works So you guys will follow me on Instagram and switch and spinner all over the channel in the description box below There's always I think as come back and watching I'm even rabbit


Yeah, my name's Frances LePage and I'm the product manager for Moodle Cloud. So, Moodle Cloud, what is it and what do we provide? Moodle Cloud is a software service version of the Moodle LMS or as we call it Moodle as a service. It's built, maintained and managed by Moodle HQ. Moodle Cloud provides our customers with the latest version of Moodle. So, as soon as a new release comes, we usually do the upgrades after the minor release, which means Moodle offers a quick, reliable, stable and secure hosting solution for educators around the world just on a smaller scale. So, who do we serve? Moodle Cloud currently serves about 213 regions, over 20,000 sites. Our top five countries at the moment are America, India, Spain, Australia and Mexico. So, we've done a little map just to show you on that. So, next up, I'm just going to talk a bit more about who our customers are and what that is sort of focused on. So, we've conducted market research over the past two years to really understand who our customer base is and what are we providing for them and what do they need. We found three common segments for our customers, where there's 25% of them who are focusing on training their staff. 30% are e-commerce. So, for example, they're selling courses to educators or businesses and we've got 45%, which is teaching in schools, colleges, universities, those sorts of things. That's just the major ones. We were able to develop personas from understanding those three segments and we use those personas to help our team make decisions about what our users' needs and requirements are. And so, our main focus over that for who we serve at Moodle Cloud is the individual educators. So, these individual educators include... What's her name? Sarah. Sorry. Sarah is our teacher, for example. You know, she's an individual educator at a small business teaching vocational students and she needs an LMS that's reliable and easy to set up without all the technical skills to host and maintain our site. As some of you know, it's not a simple process sometimes. Next up, we have Matara, who's a HR manager. Matara needs something that's reliable to be able to train her staff and ensure that her staff has access to the organisational learning information. Then we have Wally. Wally needs to sell his courses. So, for example, in his situation, he's selling to vocational individuals. So, he needs change slightly from the... He still needs something that's reliable and secure, but he needs to be able to have those payment systems to be able to sell his courses. So, what can you do with Moodle Cloud? Moodle Cloud is the Moodle LMS. So, you can utilise all the inbuilt tools and activities that Moodle has to offer. You can make the most out of your Moodle Cloud without all the technical hosting because we take care of that. So, to keep things simple and safe, of course, as Greg was just saying before, unfortunately, we don't allow our customers to have access to the database. So, you aren't able to install your own plugins and themes, but that doesn't stop you being able to use... Make the most of your Moodle Cloud site using all the great things that Moodle has in its core. So, using those great things, you can still build wonderful courses. You have access to the tools such as H5P, LTI, and Moodle activities, such as the most commonly used ones, assignment, forums and quiz. And there's cool things with the Moodle Cloud. If you have lots of files because we do have our different plan sizes, you're able to link your Moodle Cloud site to repositories such as Google Drive. You can do this by creating new projects within your Google Developer Console and add that to your Moodle Cloud site under OAuth services. And once you've added that, you can enable that under management or authentications. Pretty cool tool, really. Another amazing thing that I'm going to shout out to Paul is that we now link up to MoodleNet. Now that Moodle Cloud is on Moodle 4.0, you can directly link up your site to MoodleNet and search all the content under that. It's really quite simple. It's under any other activity. When you're searching for activities, you can find MoodleNet and you can click in there and link up to your profile, which is really awesome. Another really cool feature of Moodle Cloud, if I do say so myself, is our ready-installed document converter plugin. This enables you to automatically convert an uploaded assignment submission to PDF format for teachers to grade and grade and basically do feedback, comments, stamps, highlights, all those sort of things that you need to do within it. It's a really cool feature. As some of you might not actually know, our Moodle apps, we have access to the premium plan. This plan includes unlimited active devices for push notifications, unlimited access to offline courses, customized app features and all a lot of other cool stuff. You can check out on the website. For a lot of our users that might, their first time coming to Moodle, they are looking for a quick and easy way to set up so they don't really understand how to use Moodle. That's another awesome thing that we now have is Moodle Academy. There's some really cool courses about admin basics. There was a language one recently and all these sorts of things that help you set up using Moodle. The next thing is, once you outgrow your Moodle Cloud site, if you need something bigger, a feature that we have inbuilt in our Moodle Cloud portal is the ability to export your entire site. From that, you can go to one of our Moodle services or our Moodle partners and they can take that site, take that back up basically and get all your really cool hard work onto a new hosted service that they can then customize, add some new features, add plugins, themes for example and things like that. It's quite an easy transition and you can all do that yourself or you can ask the Moodle partners and services to help you to do that as well. I think I'm really quite ahead of time but I've talked way too far, sorry about that. What's next for Moodle Cloud? I'll run through that and try and slow down a little bit. We're really focusing on researching our users' needs and diving deeper into the individual educators and going through those personas that I was talking to you about. What do they need? I know everyone's heard about these things, course templates. For example, we've got our educator, what would they need when they first hit Moodle? They sign up for a Moodle Cloud site and they come to that page. What do they need to help them get really started? That's what we're going to be focusing on as a teacher, if you're training staff or if you're someone that wants to be selling courses. It's really going to be that starting point you land on that page and there's already things semi-built for you and it's very simple to get that set up. Our next other major thing is we want to be able to offer custom domain hosting for certain plans for us so that you can choose, could be your school or your business, those sorts of things because at the moment everything's at MoodleCloud.com and that might not serve some people. That's it, thank you. Anyone got any questions? Exercise, come on. Someone's got a question. What about the apps? It's obviously a decision that you can't add plugins to Moodle Cloud and what's the thinking behind that? Do you think that will ever change? Not, probably not for MoodleCloud to be honest. Because we're so, we're focusing on just the smaller sort of sites and you think about all the plugins that are available, there's certain ones that they really need to be maintained to be able to have that safe secure infrastructure if people start wanting to add all different things. Some of them might not be maintained and our main focus is trying to make everyone's sites run smoothly and that's why we generally offer them to the services and partners. It's a bit more detailed to go into adding different plugins. An alternative could be to perhaps provide some of the top most used and favourite plugins perhaps, but I take your point. Thanks for answering that. Yeah, definitely. Sorry to add to that. We're always thinking about what we can add to MoodleCloud that would help MoodleCloud and yeah, if there's ones that would help our personas and in that situation that are top five, the problem is everyone wants different things and there's so many options and I think it's really trying to find ones that solve many, yeah, many things. Okay, so following on from that, maybe one suggestion for one that you could include. Because I think H5P is not the actual H5P Moodle plugin, is it the one that doesn't track in MoodleCloud because there's two different sort of flavours, isn't there? Yeah, H5P that's in Moodlecore. Yeah, which is slightly different to that, doesn't track so well. So I think H5P would definitely be one top of the list to include. I think it's really popular. Yeah, you're right. H5P is always on our list. It's always. How can we improve that as well? So.


Everybody forced here rip in 2022 top transcendent collection baseball case number 10 random hit style. I See your message Joe or John for Joe Do you need us to quick quick question for you John? Do you need us to change the name on the order like completely like the shipping address and everything or just for the break? Or is it like it is just that part incorrect? So Joe W needs to be John W. All right, so We got the case right here y'all. We'll get it open bring it over here. There are 50 framed autos also go through and those will be individual hits Everything else that we're gonna random off. So there's eight other things. There's a transcendent VIP party invitation 1958 Superfracture auto one-of-one and auto patch bat knob or nameplate auto book. That's one item there It's one of those three things a Chrome four card pack with a lease one Superfactor an oversized cut auto do a call cut auto or letter patch auto a Transcendent gold Deco auto 50 card sealed base set and a one-of-one wander Franco or Vlad junior through the years auto So that's what we got there Okay, I got you. I thought you'd be I thought you'd be in for real John Anyways, here we go. John. Maybe I'm in on it Did he get your socks for Christmas because we can we can change it party invitation? Biggest chasing the cuts Like Ruth and Lincoln. I there's not full lists. It's hard to say But it's like Ruth Jackie Lincoln Whatever there's other some other big US presidents that are probably in there Sometimes it's like a Churchill Jefferson George Washington was last time as well if there's ever like a John F. Kennedy. That's always big Everything's pretty big. I mean you'll see like Bowie here in there. You'll see like Freddie Mercury sometimes That's always pretty cool. Well Andy Warhol earlier. There's like we pulled a dolly last time Pace 20 this case wider than the others 20 got a mess to clean up later Probably what Kyle's doing person on the top of it. Hey, what's up back there? That is the so this larger one is obviously oversized cut auto patch auto or dual cut auto This is the sealed pack here that is one item sealed That's going to have a super fractured inside of it at least one just three other cards as well This is the super fracture auto 1958 design super fracture auto. Watch out. Take a break Face set stay sealed same number as the case 2099.  Oh Man come on cut signature bat name plate book card. These are uh, I guess you call short printed not very many of them Yeah, we've gone through this is Literally the 10th case we've done they've all we've all only seen patch auto so far. Oh boy And Then a deco gold one-of-one auto and there are the 50 framed autos right there. Oh Man, oh man. Oh, man. It's gonna be wild mark. I'm gonna break the seal on that thing open it up Yeah, right it's sealed with a transcendent sticker I Need to show it, right? Just hold it here. Yeah, definitely asked. Well, I probably sounded the lane average, I guess I don't know because everything else is obviously not it. I mean, they're not actually you can see what it is You could read. I think you should be able to read on the back what it is, but That's all right, and honestly We're gonna get better shipping than that The thing is like I think we're gonna have to it's not it's not totally like set in the Thing so all right, let me check spots and then we're gonna get through those framed autos first. Oh My god orders are but at I and we just had like 15 orders come in 12 sold out 13 is it one? Holy cow And then there's 32 and 38 71 total spots left for tonight as Of a right now. Oh boy the Wendt brothers are here. Oh boy. Oh Geez Joe and John taking a meaning of family feud to a new level Say no Steve Harvey family feud. Let's play the feud. I Love to play the arson.  Yeah Oh, he's out. He's asking me why don't you one second guys? Sorry Figures about mid break it happens purple now The machine Albert Pujols auto one of ten Albert Pujols big Al Next up is an Alec Thomas for Kyoto 17 out of 20. Alec Thomas 17 to 20 after that Reds player here Barry Larkin 11 of 20 Barry Larkin 11 out of 20 Yeah, because it has a name on the back It junior 20 of 20 Bobby witt jr. Come on Royals put a team around this guy Come on Royals After that is a bow Jackson auto seven out of ten Probably that's where you go bad. I think yeah Bo Jackson seven out of ten So with the with that booklet there's there's a name there's there's a name on the back I'm pretty sure And it's sealed We're not gonna open it unless the person that is in chat If they're here and they hit it and they and they say that we can open it other than that It's gonna stay like that so it's in between like one of the encased cards and like a Like the pack I guess Because you can I'm pretty sure you can tell who it is and it says what it is So we'll leave it sealed unless Whoever hits it is in chat. I think that's the only safe way to go about this But there's like obviously everything else is here, but you can see the card. So there's a reason for those are in case But a booklet probably won't stay in case super long. So Yeah, I'm gonna leave it up to the owner of the card not us rookie auto Brandon Marsh one out of 20 Yeah, it's it's literally it has the tops like seal So theoretically it's the equivalent of opening like Like a panini or top sealed like mag, but the issue is is obviously you can't see the the card you can only see The the outside of the book so But that's not our place to say so unfortunately We're not gonna pressure somebody to open that either Bryce Harper 16 of 20 on the auto. Oh for sure mark for sure It's like the packs like I want to see the packs, but I also want People to get them and decide for themselves and not just like us. Just oh, here's your pack.  So It's only 99 of those packs nice Bryce It's other people's money, you know, ruby one of one rookie Bryson stocks color match big hit Good luck on this card at the ends Yeah, we go. I wanted to open up your Lewis Hamilton so bad Just take take the knife and cut it and open it up I was gonna sign the back for you pulled by The sign right there. That'd be awesome Awesome start a Cal Ripken junior auto 15 of 20 Cal Ripken Next is Carl Yastremski 9 of 15 Yash Trezemsky Green again to 15 CC sabatia auto To a 15 on the CC example of like a pack that we haven't ripped But it's I mean that the pack is similar to like Baset or something Chipper Jones 8 of 15 green auto framed auto Chippa Excuse me illegal. I Don't know what that means When the legal says it could be a lot of things so just two case left with spots guys They're both just about halfway full one is past halfway. The other is just about halfway So if you want to spot and transcend it, they're feeling quick Point five CJ Abrams rookie auto three of 20 I spell it out slowly. I how did how could I how? Why did not I remember that? Ytpm was Yash Trezemsky's typed per minute now everybody that's in this chat We'll have an inside joke for the next however however long Abrams there Green auto Cody Ballinger 11 to 15 JJ Purple Corey Segurado 2 out of 10 green auto Dave Winfield 5 out of 15 Derek Jeter auto 4 of 20 Derek Jeter 4 of 20 That's wins legend Dave Winfield Eddie Murray auto 5 out of 10 All right. Sorry guys text the lane right now Tatis auto 10 out of 10. Good luck on this Tatis a Frank Thomas auto 3 out of 15 3 of 15 Frank Thomas auto George Springer auto 6 out of 10 George Springer 6 out of 10 on the framed out of there a lot of purples recently All right All right Hunter green rookie auto 13 of 15 green green Jared Kellnick auto 7 of 15 to Jared Kellnick. It's the first Kelnick. I've seen Hmm skew of autos here Red Sox jaren Duran rookie auto 8 of 10 Name color match Jaren Duran 8 of 10. All right. Sorry a bit behind guys probably make up a little bit of time here Probably get to the next few a little faster Johnny Bench auto 6 of 15. Next card is an auto Any more bold predictions from a Shane Stradamus over there VIP Shane over there 18 at 20 auto Jonathan India Jonathan India Ruby Louise Robert one of one That's an awesome card That's a good that's a one to get good one again. They're in it for sure. Good luck everybody one of one Ruby Boyle Louise Robert auto La Pantera Martin McGuire auto 12 at a 20 your nickname in high school changed for Domus Miguel Cabrera 3 of 10 vertical Miguel Cabrera very nice card there, too Next is Schmitty 4 of 10 purple foil auto Mike Schmidt means we got another Mike here That's trout isn't it? Yeah, it is Mike trout 3 of 10 That's a goldfish right there Gold framed fish rookie out of Nicoladullo 11 of 20 Nolan Ryan 9 of 10 purple auto. Oh, no, Rob. Oh, no rookie out of O'Neill cruise 12 of 15 Cruiserino get that one bagged up. This is an Aussie Smith 4 15 the wizard auto Think a purple Shohei to purple trout purple Shohei. There's Aussie 4 15 Paul Goldschmidt 1 of 15 green on the framed auto Goldy reigning NL MVP had a good day at the play yesterday as well Pita Lonzo 19 at 20 framed auto Polar Pete MVP contender last year Randy Johnson auto 10 out of 15 Randy Johnson 10 of 15 Robin yon 15 of 15 on the auto Count on yount Purple next Rod Carew auto 5 out of 10 whoo 5 out of 10 20 Ronald Acuna jr. 2020 bookend Great hit on the Acuna Rhino auto 15 of 15 Ryan Sandberg How to fame a rock heel and Clark Ryan Sandberg on a 15 of 15 rookie Shane Boz auto 9 of 20 calling Ronald Acuna jr. Best outfielder in the NL East Shohei Otani 8 of 20 Shohei Otani 8 of 20 on the auto. Good luck on that one everybody of course Or if you auto Spencer Torkelson 7 of 20 Illegal might might be injured that was a big stretch God trade Turner auto 14 of 15 point don't jump on his side Mike The variation is just horizontal Vladdie jr. 13 out of 15 The emerald auto there 13 of 15 Vladdie. It's gonna be a wonder it is 17 at 20 wander Franco framed rookie auto. Would you have muted Rob? Who you muting? We're going through him quick Well, it's like there's like four or five guarantee and then sometimes just like four or five more all right Start with the through the years Through the years either wonder of Ladi or we've seen both we've seen both either wander of Ladi One of one that's a blue J's helmet. So it is a Vladdie jr. That's a cool year 1999 tops Through the years out of Vladimir Guerrero jr. It's always good luck on all the one of ones here not just this one 1999 good Prince on that's the Deco. We'll go Deco now.  I'm not damaged by like something loose inside there Just wanted to point that out probably just a piece of paper probably doing nothing to the card at all, but Julio Rodriguez rookie auto one of one is sealed.  Oh my god. That's one of the cards we pulled today We'll do a super fracture and then we'll do the book. We haven't seen the book yet Super Fractor eyes Harper 1958 Super Fractor auto What a monster holy cow, man. All right, we're cooking now Finally got a book too. So again This next one is sealed inside that slider box We're not going to open that booklet unless it'll be after the break it We're not gonna open the booklet unless you ever wins it and the random is here and it wants it to be open That's it Because it is like I said it has like a transcendent like sicker steel on it sticker seal so you can see Yeah, it goes all the way around as well. So It is a cut signature bat nameplate book card bat nameplate Kirby Puckett. Oh my god Way What? Harper super Deco J rod Kirby Puckett cut signature bat nameplate book card Man That's freaking huge Yes, so again, you can see the stickers go all the way around here. Oh, man But again, whoever gets one of the random if you want us to open it, we will but it'll be after the break Cuz yeah, oh my god. Oh my god. I hope so, but honestly, please do not open it because up here pressure Do not if you feel better. I keep it sealed open it yourself or whatever or sound like that Then you do that but anyway on to the last hit of the break Let's see a dual cut one time. So it's either. Oh Oh, what is this? Oh man, I See Dodger script. Oh Cos god cause gone. We're alone everybody. We're alone. Oh, man. Okay No, yes Jackie Robinson Oversized cut signature one-of-one Unreal do it went back to back Frederick. Oh, it's Frederick. Let's Jackie Robinson that Oh, man. Yeah. Chills again. Chills again. Oh my god Okay Okay All right, okay God Everything like we have big frame dollars everything past the frame dollars was Pretty legendary right there. Oh God just make sure you click out of the box when you're done Sampled the Jackie and Bowman transcendent.  Oh my god Okay, okay. Yep One of the most important names in American history okay We're gonna random the names and then the hits the same amount of times and put them side by side to see Who gets what want to look at one more thing and then we'll do this and again Whoever hits the Kirby if you're here and you want us to open it. We will but that's it. We'll leave it sealed otherwise nine five four nine times five and four the luck one two three four five six seven eight nine Jason is on the top and the bottom and then they hits nine times one Two three four five six seven eight nine Tray Turner down to the Jackie That's Jason Jason Congrats Jason. Thank you again, but as you can see a lot of spots not just in this but today Okay, so Jason has the Tray Turner Acunia Ozzie Abrams Marsh bench John A with the Shane Boz Jason C has the Alec Thomas Martin McGuire Bobby wits Rod Carew yount Ripken Sandberg Kirby Puckett name played auto cut signature book. It's wild again at stay and sealed for now And the epitol on so John A getting the four card pack congrats on that John The four card pack with the least one super which is also going to get get sent to you sealed And then I believe Jason C is the rest of them here Dave Winfield Barry Larkin Nolan Ryan Eddie Murray Sabathia trout Springer Jeter the deco gold J rod Chipper Luba ruby framed auto one of one Corey seager Vlad jr. Through the years one of one Frank Thomas the base set Lidolo Beltray Ballinger Bryson Stott rookie auto ruby one of one Pools Harper Wander Kelnick Tatis Goldie The invitation the Otani Jonathan India O'Neill Cruz Jaren Durand Yastremsky Bryce Harper Superfractor Hunter Green Vladdy jr. Mike Schmidt Randy Johnson Miguel Cabrera Spencer Torkelson Bo Jackson Aaron judge and The Jackie Robinson that was pretty cool, man


I believe that the goal of every crossover game is to have a roster so good that you can't believe it's actually real at first. And after quite some time, we have received another one of these legendary crossover games in the form of multiverses. I think so the fact that WB Games is generously sponsoring this video, we were able to actually go in and play and record a bit early. And of course, by we, I do mean the three idiots, and my friend Afro sends you, because this game does focus on 2v2, meaning it is the perfect game for settling a score amongst your friends. And right now, the only thing I'm trying to prove is that out of all of us, I am the best when it comes to this game. Alright, I gotta start with Shaggy. Okay, baby, let's go. It's us, truly, truly it's us, Afro. I knew when I heard that there was an impactful, dynamic 2v2 system, I knew it had to be us. Yo, Dijon, you good over there? I can't. I'm physically incapable of him. I'm talking about him. God, the collective IQ of the enemy team has to be like three. What do you mean, Buzz Buddies a genius? That man's got carrots for days! I kind of forgot it was rabbit season out here. Wait a minute. Okay, the rules are simple. The first of three ringouts wins, and I'm going to win. We shouldn't be fighting these individuals. They're crazy. Let's go, I'm full power. Oh my God. Oh, I got my scooby-snack as well. There's a Wazard with, wow! There's a Wazard. Bro, y'all ever watched Wazards of Waver the Place? Oh my God. There's a weather advisory. There's a tornado on the loose.  I'm going to be in the struggle. Let me power up. Let me get some scooby-snacks coming in, bro. Get these scooby-snacks. Actually, moin? Oh, bugs took them. Bro, I want some filet mignon. Filet mignon. Sandwich. Bro, I know you ain't laughing. Bro, I wasn't even laughing that much, bro. It was kind of funny. Oh, we can take your scooby-snacks. Alright, but you don't need to announce that to the world. Bro, here we go. Damn, I got hands. I am tornado.  Boom! Boom! Now wait, this is my video. Get him out. Okay, so not my day. Oh, wait, wait. Let's get a quick double kill turning around. Does your plan include tornado?  What?  Bro, why did that last three days take you to eight weeks? Look at that, bro. That'll mad load. Oh, wait, look at that, bro. Hell, let's finish this. Oh, let's finish this, dude. No, no, no, no. Just go. Let's finish this, dude. Why are you laughing, bro? Bugs Bunny, kiss me. What happened? Why was I so enamored with Bugs Bunny? He ain't even all that good looking. Hold still, brother. Wait, wait, wait. What? What's going? What's going? Oh, we got him. We got him. What's going? What's going? What's going? I'm alone. I'm alone. Why do you walk like he's sneaking into somebody's room tonight? Damn, I'm hungry. Borns.  Did Shaggy just sneeze in his sandwich? I know you ain't talking. Bro, I've been blowing my nose. I got to use something. Oh, my God. Bro, I'm going Shaggy for this first, first of two, and then you all get to my real main. Let's go. Let's go. This is exactly what I need to see. Oh, and these two, they probably... It was going to be confusing. I didn't. We're not going to guess that. Bro, I got three. Bro, there's three bitches on the screen for real. Yo, this is actually POV three dudes. That's where the hose at. And then when one comes around... Your mother's going after it. I love that loading thing. Man, we'd be eaten for real. I like how Shaggy opens every match by saying, you have no idea the power that's inside of you. That was a good idea. Like, if you don't get back to Dragon Ball Fighters, there's so many Scooby Snacks on the map. Bro, I'm so confused. I don't know who I was for a second, bro. I'm looking at the blue. I don't even know who I'm fighting. Don't come up here. I said don't come up here. I said don't come up here, bro. Each of us up here, bro, wherever you want to go, brother. You don't got to say it like Scooby. That was me. Yeah, I'd be fighting after all half this match, bro. I'm confused. No! Oh, my God. Is that the Game of Thrones banner? Nah, in your wildest dreams, maybe. Oh, he got a bomb on his ankle. He got a bomb on his ankle. What you don't understand about me is I possess the Super Sandwich. I was not a Rhyme Sorrow. Go! Please. We lost the three stock, yeah. But you're going to lose the whole game. Oh, Dion, you were getting the hands is what I wish I could say to you. What are you talking about?    I get confused, man. I'm literally not. I'm the only non-Shaggy. How did you get confused, idiot? Because all I did was... Hey! Look at us. Look at us. What?  My hands are up. Oh, the crowd goes wild. All right, so that's like one, two out of three, though. I'm not losing again. That's one, two out of three. Good math. Okay, but there was nothing wrong with my math. I know, but you know you were confused as you put that sentence together. All right, let me go to Dottles team. Let's get some dubs, bro. I got you. Hey, you're working with Coyote Cold here. You should feel honored. Wow. His icon's the mystery machine. I better be careful. Oh, I unlocked a new reward.  Okay, but I was pretty happy about it. Relax. On everybody, everybody at home. Look at Jerry. Jerry, you can hit the like button. That was well timed on my screen. I think it's time to go ahead. Go ahead. Hit the like button. Yeah, I'm shaking his hand, but it's not genuine. It's a front. That's like me when I... Did you see Batman? No, I saw Velma getting killed. Oh, I saw Batman dropping stuff out of his belt. Anyway, this is my real main, bro. Yo, I hope we can get some... Bro, shout out, Tony Hawk. Oh, my goodness. Ah, there's a trap there.  Oh, look at this stuff. Oh, look at Dumb. He landed right on my trap. He was gonna get him some cheese. He was gonna get him some cheese.  I am a house, and I will be for quite some time. Oh, I'm a horse. I got you.  I'm set it away. Serena Williams! Stop! I will die, dude.  If you... Get out of my game. What?  No, that was me. That was me. Okay, but can I say it was me? It's my video. Yo, Rive is way too low. I'm about to kick-flip off his head again.  Damn, I scored him off the ground. Shout out, Velma. All right. Now you just make me stinkin' mad, Doug. Trick shot. One more time. I don't miss. I don't miss. I wanna be sick. We got a three-sock alert. Local three-up. Nah, nah, nah, nah. Are we gonna combine something? All right. We still got one audio time. Hold on. If we just get fit off the stage... Oh, we playing tennis. I can't. Please, please stay on, bro. I will handle this if Finn gets off the stage. Off the stage, bro. We in the same show. There you go. Off the stage. Dino, you mad.  I'm focusing. I know you are. Oh, cook him. Cook him. Let's go. Let's go. Let's go. Let's go.  Your winner is me. Hey, now let's try videos, bro. I kind of went crazy that time. Wait a second, bro, because I'm like a solid six foot five on a bad day. All right. Now I gotta go with my true actual man. All right, bro. Let's get that whammin' baller, then. Team woman, let's go. People think that this is a style. I actually ran out of blue hair dye and just had to go to my red. Tough crowd.  That was my favorite part of the video. Yo, jinkies. Yo, Dion, get in front of me so I can talk to you. I missed. I missed. Bro, I'm a bargain. I got a clue. Dion, if I assemble all five clues, I'll be able to call the police. Oh, my God. He's good. He's good. He knows. I'm getting destroyed. Oh, my God. Hey, we got one. All right. I wasted a stock. I didn't even have a high percentage, bro. Please, bro. That's my clue. Dion, I'm getting these clues, bro. The police are on their way. We just got to hold out.  Oh, I have the lasso juice. Bam, bam, bam, bam, bam, bam. Damn. Wait, I've got the police on speed. Get him. Yeah, that one right there, officer. Get him. Yeah, that one right there. Damn, bro. Officer, you got to get him. God damn. We'll do it ourselves. I know you ain't laughing. I know you ain't laughing. I said I know you. I am Wonder Woman. It went wrong. Hold on. I got to hit him with the glasses. No. Yeah. That's what happens, bro. That's what happens. Let's go. Let's go. I'm getting spots for days. This is my video now, except it's not. But I have highlights. Dion, don't die. Dion, don't die. Dion, don't die. Dion, don't die. Dion, don't die. Dion, don't die. I was happy. Hey, bro. Hey, bro. All they got to see is the highlights, brother. But what you mean the highlights? It's one more. We better get our act together, bro. You know what? The comment section, I hear you. You want it. The Rain Dog. I'll show it to you. And I can only be one combination of characters with that. Everybody loves a good Rain Dog. Arv? Everybody loves a good Rain Dog-Taz combination.  That's what I'm saying. That's what I'm saying. Oh, my God. There's a picture of the Joker in the background. It's not a hint. Oh, God. Alfred. Oh, God. Alfred's standing on the stage. Alfred. Read a comic, bro. Sorry. Sorry. You wish. Oh, no, Dion. It's the three-stock alert. It's for them, I hope. Rain Dog. Get over here. Damn. They kind of got combos. I kind of underestimated them. Damn. Wait a minute. Me and Dion kind of got combos. Bro, calm. I'm kidding. Are you actually not seeing my Rain Dog? Are you not seeing what I'm doing? Respectfully, I don't care what you're doing because I know what I'm doing. Bro, I'm good, bro. I'm good. I'm good. Let's go. Let's go. Goddamn. I am just hungry. I am just hungry. I just want to consume. Bro, you got a whole shield. That's it. I'm throwing apple cores at you. I'm enraged. You really made it mad now. Why are you not dead yet? Bro, because we're good at the game.   Where are you going? You got to play aggressively. I can bring you back, except for there, because I was doing like, I was talking.  That's what I'm saying. Fight back. Deon, play aggressive. He's playing aggressive. Aggressive. Oh, we would have pulled that off. We would have been remembered as his king. Go away. We're kings.  We got it. We got it. Deon, careful. He's having his moment. Deon, this is my video. This is our video, bro. You're right. What? That's it. That's why it's our video. Yo, look at us. Let's get started with it. Rain Dog and Friends. Yo, why is this game called Multiverses and not Rain Dog and Friends? Look at my damage. Look at my numbers. Look at the end of the video. Thank you for sponsoring, by the way. Bye.


to our lecture series, Math 3130, Modern Geometries for Students at Southern Utah University. As usual, I'll be your professor today, Dr. Angela Missildine. In lecture 14, we're going to start talking about the congruence axioms. So Hilbert, as he axiomized Euclidean geometry, put his many axioms into one of several groups, two of which we've already talked about. The incidence axioms we've talked about previously and the between the axioms we also talked about already in this lecture series. So the third family of axioms that we're going to discuss are the so-called congruence axioms. Now, the incidence and between this axioms both came into groups of four. The congruence axioms are actually, there's six axioms total. And so actually our discussion is going to break it up over two lectures. In this lecture, number 14, we're going to talk about the first three congruence axioms that have to do with the notion of congruence of line segments. And then the other three congruence axioms we'll discuss in the next lecture, which those deal with the, well, three axioms of congruence related to the idea of congruence of angles. And so that gives us a natural dichotomy between congruence of segments and congruence of angles. The two are related to each other, of course, but we will define those a little bit later. So with Hilbert's axioms of congruence, we introduced two new undefined terms. The first one, well, actually both of the words are the same, but they do have a slightly different meaning. So in this video, we'll give us one of the undefined terms. The other one will come next time, of course. So we introduce an undefined term called congruent. And this is a relationship between line segments. So we say that a line segment AB and a line segment CD can be congruent. And we would denote that using the following notation right there. AB is congruent to CD. So just like any undefined terms, without any axioms, it means nothing. It's open to complete interpretation. All that we have here is that congruent is a binary relation on line segments. Okay. So we'll introduce the first three axioms of congruence, which say something about what it means for two segments to be congruent to each other. Like always, when we talk about these axioms, these Hilbert's axioms for including geometry, we're going to attach some names to them so that it'll be easier for us to describe in this lecture series. But this naming system by no means is universal. All right. So with that, let's start with the first three axioms of congruence. So Hilbert's axiom C1, which we will refer to as segment translation reads as the following. Given two distinct points A and B and a ray emanating from some other point A prime, there exists a unique point B prime that's on the ray R such that AB is congruent to A prime, B prime as segments. In particular, on the ray AB, that's a unique point. That is B prime is equal to B. All right. So before we talk about the other two axioms, I want to try to unpack this one a little bit. So we start off with two distinct points. And with those points, we're thinking of it, we have a line segment, right? So we have these points A and B, they're distinct. Any two pair of points determine a line. So there is a line, there is a line between the two. And even when I say where it's between, we're assuming as we define these axioms, notions of betweenness, notions of incidence, they're very much in play right here. And so then suppose we have some ray, some ray R, which doesn't necessarily have anything to do with the line segment. It could, they could be co-linear, but they don't necessarily have to be. We have some ray R, but we do know the vertex of the ray is the point A prime, like so. So this is our setup. We have a segment AB, we have a ray whose vertex is given as A prime. So then what the what the segment translation acts and guarantees is that on this ray, there exists a unique point. This uniqueness is important here. We'll use this all the time. There's a unique point B prime that lives on the ray, R here, such that the line segment AB is congruent to the line segment A prime B prime. And we'll often use this little naming convention that if we have a correspondence, a congruence of segments or angles or whatever, we'll often label the same vertices, the same points using the same Roman letter, but we might add something like a little mark like a prime or whatever to make that correspondence more apparent, of course, to the viewer here. All right. So the segment translation then gives us that if we have a segment and we have a ray, we can then find a segment on that ray that's congruent to the other one. And so this is where it gets the name segment translation. The idea is, oh, it's as if we could move this segment onto the ray. And so in essence, we can move congruent segments anywhere we want throughout the geometry. But like I said, this point B is unique. There isn't more than one point that can accomplish the same thing. If we had some other points, B double prime, B triple prime, or maybe B prime is between them or something, right? This is the only, this is the only segment on R that'll be congruent to AB. If you pick some other point, not going to happen. So there's a very important uniqueness statement put inside of this. In particular, of course, if you were to take the ray that emanates from A in the direction of B, right? So if you're looking at this ray right here, then the uniqueness statement tells us that if you translate the segment AB onto the ray AB, this ray right here, then of course, this unique point that we were guaranteed must have been the point we started off with. So this uniqueness statement is built into the cake here. We'll actually use this a lot. In particular, the uniqueness statement of segment translation is very, very, very important. Okay. So let's now talk about the second congruence axiom of Hilbert. This is axiom C2, for which we will call this transitivity of segment congruence, which as the name seems to suggest, we do have, since congruence is a binary relation, we assume that this binary relation is transitive. So if the segment AB is congruent to A prime B prime, and if the segment A prime B prime is congruent to the segment A double prime B double prime, then we can conclude that the segment AB is congruent to A double prime B double prime. So with our usual intuitive notion of congruence, this should be satisfied, right? In fact, we might think that congruence is actually an equivalence relation. We'll say some more about this in just a moment. But the second axiom of congruence assumes that congruence of segments is a transitive relation. We will see that it's an equivalence relation. We'll prove that's reflexive and symmetric in just a moment. Okay. But before doing that, let's also talk about axiom C3, which we will call segment addition, which tells us if we have three points AB and C, these are all three points on a line. And so such that there's a between this relationship, B is between A and C. So I want you to be aware here that we're trying to make a connection between the congruence notion of segments with betweenness, because these are some undefined terms we put into play earlier, right? I mentioned as we talked about segment translation, how there's these notions of incidence playing around there, right? That you have these line segments, you have these rays, these are all parts of lines. There's of course a unique line determined by A and B, there's unique line determined by A prime and B prime. So segment translation does make a connection between congruence of segments to lines. A segment addition is primarily going to allow us to connect congruence of segments to the notion of betweenness that we studied previously with order to geometries. So we have three points AB and C, such that B is between A and C. And then we have three other points, A prime, B prime, C prime, that live on a different line, L prime, right? Such that B prime is between A prime and C prime. So notice what's of course happening here, right? This naming convention I said before, the point A coincides with A prime, B coincides with B prime, C coincides with C prime. This is exactly what I mentioned earlier, L coincides with L prime. There's this natural correspondence between the betweenness there, all right? So those are just the assumptions. And so then segment addition tells us that if A prime, excuse me, if AB is congruent to A prime, B prime as segments, and BC is congruent to B prime, C prime as segments, then the segment AC is congruent to the segment A prime, C prime. So let's illustrate exactly what we have in mind here. So we have some line L for which there are three points on this line, A, B, and C, for which B is between A and C as illustrated. We have some other line that we can see right here. This is called L prime. And it contains three points as well. Now of course with our naming convention, we'll have A prime, B prime, and C prime. So what segment addition then tells us is that if the segment AB is congruent to the segment A prime, B prime, and if the segment BC is congruent to B prime, C prime, you'll see that we'll have to put these little tick marks on a segment to suggest it's congruent to another one. This is a very common geometric convention. So if this segment is congruent to that one and this segment is congruent to that one, notice that the union of these two segments is AC and the union of these two segments is A prime, C prime. Well, if the two parts are congruent to each other, then it turns out that these ones are going to be congruent to each other as well. And so that's why we call it segment addition. So the idea is if we have a congruence between the pieces, then when we put them together, when we take their union, we will retain congruence. And this is a foreshadowing to the idea of addition that we will talk about later on, because after all, if these segments have a length to them, because in Euclidean Geometry, for example, we say that two line segments are congruent if the distance between their endpoints are the same. So we can use the metric, the distance function of the geometry defined segment congruence. The way that we've talked about congruence here, we don't need distance, because congruence is just an undefined term, we can interpret it in many different ways. Distance is one possible interpretation, that's how you do it in Euclidean Geometry. But foreshadowing that, right? If these two distances were the same, and if these two distances were the same, then the sum of the distances must be the same as well. And so that's if you think about it in terms of distance, that's why we call it segment addition. So now summarizing what we have here, like I said earlier, axioms C4, C5, and C6 all relate to congruence of angles, and we're going to list them next time. But despite not being explicitly listing the axioms, all of the axioms of congruence, we are ready to define what a congruence geometry is. We say that in ordered geometry, remember what an ordered geometry is. An ordered geometry, it's an incidence geometry that satisfies Hilbert's four axioms of betweenness. An incidence geometry of course is a geometry that satisfies Hilbert's four axioms of incidence. So an ordered geometry has the four incidence axioms, it satisfies the four between this axioms, and then we say that a congruence geometry will be an ordered geometry that satisfies the six congruence axioms, the three we just discussed, plus the three that we haven't yet been explicit about as well. So congruence geometry means that we have the four incidence axioms between the axioms and the six congruence axioms. We call this a congruence geometry. Now, I want to relate this to the very, well, relatable topic of what's called a neutral geometry, which we will define later on. Neutral geometry is very similar to congruence geometry. A lot of people who study geometry, when they study neutral geometry, a lot of what they're studying is actually congruence geometry. The main difference is that the neutral geometry will also have a notion of continuity for which we haven't introduced yet. We'll do that, of course, later on. And then, so a lot of what people call neutral geometry is really just congruence geometry, because if you don't use continuity, it's a congruence geometry, not just a neutral geometry. So we're going to delay our introduction of the continuity axiom until we really need it so that we can develop this theory of a congruence geometry. All right. So I mentioned earlier when we talked about the transitivity axiom for segment congruence that it turns out that congruence of segments is, in fact, an equivalence relation. Well, why is that? Well, we have transitivity. We're taking that as an axiom. But it turns out that the symmetric property and the reflexive property can be proven using the axioms we already have in play here. So our proposition we're going to prove here is that, in fact, the congruence of segments is a symmetric relationship. So imagine we have four points, a, b, c, d, in a congruence geometry. If the segment a, b is congruent to c, d, then that means that the segment c, d is congruent to a, b. So we want to prove that it's symmetric. And so this is going to follow by using segment translation and transitivity of congruence. So let's first start off with segment translation. I guess I should first start off with our segments here. So we have our segment a, b. We have our segment c, d. So maybe something like this. Let me label it here, of course. So we have a, b right here. We have b, d right here. And then we're going to have c, d right here. And we're going to have, there you go. And so we know by assumption that a, b is congruent to c, d. That's an important observation in this consideration here. All right. So by segment translation, there exists a unique point. We could call it b prime that's on the ray a, b, such that c, d is congruent to a, b. So what we're going to do is think about this line segment. It could be extended, of course, the extension axiom from between us. We can extend this into some ray, right? Think of the whole ray. Well, by segment translation, there's a unique point, call it b prime, that lives on this, that lives on this ray, such that the segment a, b prime is then congruent to c, d. I actually should write the other way around because we haven't yet proven that this thing is symmetric. So that c, d is congruent to a prime, a, b prime, like so. Okay. And so by, so that's what we get. We get this point b prime with that property. But by transitivity of congruence, right, this is what we assumed. We know that a, b is congruent to c, d. We know that c, d is congruent to a, b prime. So then we have to conclude that a, b is congruent to a, b prime. Okay. But a, b and a, b prime live on the same ray. They emanate from the same point. And so by the uniqueness statement that's part of segment translation, it's got to be that a prime and b prime are actually one in the same point. And therefore we get that c prime is actually congruent to a, b prime. Thus proving, proving this statement right here that a, c, d is congruent to a, b. So we can see very quickly here using transitivity and translation, of course, that a, that this relationship of congruence is a symmetric relationship between them. The last property we need to be in equivalence relation, so we need to be reflexive. But that actually goes back to the very last sentence in segment translation where it said when you in particular on the ray a, b, on the ray a, b, if you were to translate the segment a, b back onto itself, yeah, you're going to get some point a, b prime, but you were told very explicitly that this point is in fact, this new point b prime was actually the point you already had here. So you translate a segment onto itself, you get back the original segment. And since a, b is congruent to a, b prime, and since b prime equals b, it's reflexive. So the reflexive property is built into a segment translation, it's not a completely explicit, but it's there. Transitivity we take as a maximum. And then thirdly, some symmetry we can improve using this translation action, which has reflexivity plus a little bit extra and then transitivity. And so we do get that congruence of segments is a equivalence relation.