Can you prove that these two triangles are congruent? First off, let's go through and name the two triangles. So is it possible for us to prove that ABD and CBD are congruent? Well, these tick marks right here show me that AB and CB are congruent. Also, I've got a right angle right in there. And if that's a right angle, well, this angle and that angle, they're both right angles because we've got some perpendicular lines. Well, perpendicular lines make right angles and right angles are always congruent to each other. So that means angle ABD. So right now we have a pair of sides and a pair of angles. Then notice that this side length, BD, is a shared side. It's shared in both of the triangles. So that means in triangle ABD and CBD it's got to be the same in both of them. So yes, we can prove that these two triangles are congruent and we can prove it because of side angle and then that shared side. So we can prove that these two triangles are congruent using the side angle side there. What about these? Can we prove that these two triangles are congruent? First off, let's name them. So we have triangle DEF and DGF. Well, let's figure this out. We've got a pair of sides that are congruent that refers to these segments. So let's label those. We've also got a pair of angles that are congruent. Those maybe I'll just number them angle 1 and angle 2. So now we have a pair of sides and a pair of angles. We also have, just like in that previous example, we've got this shared side up the middle, DF. So that means that in both triangles DF will be congruent to itself. So we've got a pair of sides, a pair of angles and we've got that shared side. So it seems like this might follow side angle side. However, the angles, angle 1 and angle 2 are not included angles. And again, just a reminder of the definition of an included angle. The included angle must touch both sides that we know about or that we care about. In other words, angle 1, in order for us to use angle 1 as an included angle, did I say angle or side? In order for us to use angle 1 as an included angle, it would have to be created with this segment EF, but it's not.  And likewise, angle 2 doesn't touch segment GF. So these might be congruent, they might not be congruent. We can't prove that they're congruent. So they're not provable. Let's try another example. What about these triangles? Let's name them first. So we've got DEF and GHF. So what does it mean for two segments to bisect each other? Well bisect means cut in half. And so each of these segments is cutting the other one in half. I know EH is bisecting DG. So that means EH is doing the cutting and DG is being cut. In other words, DG is cut into two equal parts. And then also, since they bisect each other, DG bisects EH. In other words, EH is cut right in half. So I have two pairs of congruent segments that come from this fact. And then one last thing, whenever we have lines that intersect, we create these vertical angles. So I could talk about angle DFE and angle HFG. Vertical angles are always congruent. And so that means that those two angles are congruent. So DFE. So we have two pairs of sides, the reds, the greens, and a pair of angles. So it's possible that we can use side angle side. The only thing that's left to check is are these blue angles, are they the included angles? Well, how can we check? The way that we can check is the blue angle connected to both pairs of sides that we know about. In this case, they are. I see that blue angle touches both the red and the green. And as a result, that blue angle is made up of both of these sides that we know something about. So yes indeed, these triangles are indeed congruent, and they are congruent by SAS. How about these triangles? Can you prove that they're congruent? Well, I got one pair of sides. I got two pairs of sides. And I got the shared side up the middle, US. And so that means yes indeed, I can prove that these triangles are congruent by side, side, side. So here we have congruent triangles. Let's try another. All right, are these two triangles congruent? So it looks like from the drawing, we have that angle U and angle R are congruent. We know that T is the midpoint of RU. And RU refers to this segment from R to U. And so T is the midpoint, means that these segments are congruent in length. So we have a pair of angles. We have a pair of sides. We need one more pair of angles in order for these pairs of triangles to be congruent. We have intersecting lines, which means vertical angles are produced and vertical angles are always congruent. And so that means we have angle, side, angle. And so therefore we can prove that these two triangles are indeed congruent by ASA. Let's try one more example. Can we prove that these two triangles are congruent? Well, let's figure out the given information. We've got a given pair of angles, angle N and angle L are congruent. I got a pair of segments, pair of sides that are congruent, JK and MK. And the way that the triangles are drawn, we've got a pair of intersecting lines, sorry, intersecting line segments. And whenever line segments or lines intersect, we make vertical angles. And vertical angles, of course, are congruent. So we have two pairs of angles and a pair of sides. We have a choice between angle, side, angle or angle, angle, side. Which one do we pick? Well, the question is, is the side, is it included or not? And by included, I mean, is that side touching both of the angles? Well, JK is only connected to one pair of angles. It's kind of leaving angle N all by itself. Likewise, segment MK is connected to this middle angle, but it sort of leaves angle J by itself. So that means the sides are not included, but we can prove that the two triangles are congruent by angle, angle, side.


Listen, it's the message right here.  Cause I just want to build with you. Black girl tell me how you really feel. I want to keep it real with you. I want to live better, eat better. I want to love better, sleep better. Yeah, I want to feel so aligned. Are men and women equal? In what way? You tell me. You can go whichever way you want. These are very broad questions. Intentionally broad. They're all broad. OK, OK, I see what's going on. I see what's going on. Are men and women equal? In some ways, yes. In other ways, no. Like I feel like men and women can balance one another as far as like what men can do some things women can't do and what women can do, men can do. I feel like we're very like yin and yang. We can balance each other very well. But in some ways, as far as like what society means, I feel like men are typically more superior according to society because men typically get paid more. And men typically are listened to quicker than women are. It's just a lot of things that society gives to men that women kind of have to fight for, kind of have to work their way up towards just to get a balance the same as men naturally get. That makes sense. Yeah, it does. Do you think there is, like in a modern context, do you feel like there is a battle of the sexes, like one side trying to show the other side that I'm better than you or trying to prove that, you know what I mean? Yeah, I probably, yeah. I would say so because I feel like I'm not going to say all men because that's a general statement. But I feel like a good bit of men, they do deem themselves as superior because of what society has instilled for a long time. And so women are now coming up and saying, well, why is he doing the same job that I'm doing?  Or why does he get to say what he feels and he's seen as being opinionated and strong. But when I try to do that, I'm emotional and I need to calm down and doing too much. So it's just like, I think there is a battle because things are kind of shifting and I think things are wanting, as far as society is wanting things to be more equal. So I think there is kind of the battle. Women are like, nah. So with the pay gap thing, is that a thing? It is a thing. OK, explain that. It's a thing. I'm not going to say I have experience, but I have experience of basically a guy who's just coming into a job that I had. No experience. I have been there for years and started at a certain wage. He came in with no experience and automatically made like $3 more than I did. And I didn't find out until later on. I'm just like, what's the, not quite understanding. So they did a study on it. They did a study on it. And part of the reason that is, so it's two main reasons that I'm not going to go super deep because I'm not that smart, but one of the reasons is women tend to not negotiate. So there's a chance, especially if it was a white dude. He probably came in saying I want $3 extra than whatever you guys are offering. Women tend to not negotiate. The second reason for the pay gap is that men usually choose jobs that pay more than women. And those jobs tend to be riskier. Those jobs tend to be in STEM and things like that, whereas women tend to go to humanities. Those jobs don't pay as much. But the third thing, too, is employers recognize or think that men are more willing to throw themselves at their work than women. Like women prioritize later on to have kids, I need maternity leave, things like that. And that gives men leverage to demand more money. So that's what the pay gap is. It's not actually that men are making more money than women doing the same thing the same way. Thoughts? But I think it is. But that is what it is. Like, yeah, all those reasons exist. When you look on paper, Tommy's making this amount of money and Julia over here is making $3 or $4 less regardless of. But context matters, right? No, when it comes to paychecks, it doesn't. OK, let me give you an example. When it comes to payday, he's still got paid more than me. Let me give you an example. So one of the big debates is the WNBA. They are demanding that they should make just as much as the NBA. Let's talk about it. Why? They're doing the same thing. OK, now I will have full disclosure in saying I am not a sports person. So I know very basic knowledge. They're doing the same thing, aren't they? No. They're not both playing basketball? What is the women doing? Playing women's basketball. No, no, no, no. But fundamentally, the game is the same, is it not? Do they have different roles? Yes. The three-point line is further in men. The quarters are different. But ultimately, the reason women get paid, the female basketball players get paid less is because if you look at a WNBA game, the bleachers are like 25% full. No, that's sad. Yeah. They deserve support too, that's sad. So the salary is a consequence of the support. The support isn't a consequence of the salary. So why should Candice Parker get paid as much as LeBron James? Well, I still think at the end of the day, regardless, they're still doing the same thing. No, but what I'm saying is where does the money come from to pay Candice Parker? I don't know where money comes from to pay them. Is it like, as far as basketball goes, their money comes strictly from ticket sales and fans and all that? It's ticket sales. It's endorsement deals. Yeah, you say both of those things. Ticket sales and endorsement deals, right? So if I am drafting a player and he can get me ticket sales and he is a highly sought after player, he's going to make more money. Whereas nobody's watching WNBA. And what's ironic about it, even the women who complain that WNBA players don't get paid enough, don't go to WNBA teams, don't watch WNBA. So where is this money supposed to come from? It sounds like they need to get creative. Or it sounds like a marketing challenge, maybe. For who? Like, why? Maybe they need to figure out, I don't know, what are the things where they get a bunch of different people from different demographics and they do like a, is it a study where they ask questions and they try to get like a focus group? Yeah, a focus group. Maybe they need to do some focus groups and figure out why people don't want to go. It's not exciting. They've done that. It's not exciting. Why is it not exciting? Because I would rather pay to watch LeBron James dunk on somebody. Do women not dunk? No. You're talking none of them. Like two of them dunk. And it's not like a... I'm not knowledgeable enough in the sport to know. Yeah, that's what I'm putting you on. It's not impressive at all. Like watching a WNBA game is like, it's not even like some high school teams could beat WNBA players. I don't know.  That's just a consequence of like the physical differences between men and women. So, and I think that's a good example of the pay gap being more nuanced than just women shouldn't get paid as much. It's like, where is the money supposed to come from? And what's ironic is, even in the instances when NBA players don't get paid as much, even in the instances when NBA players have like tweeted out, hey, y'all go support these WNBA players. Or like one time, a player tweeted like, yo, number two on this WNBA team is nice. And she got mad. She was like, I have a name, this and that. And people were like, he's trying to help you. He's trying to expose you to a larger audience, but there's like a pomposity and like an audacity that like, I'm just as good and not better than you. Because I mean, don't they have to go through the same things that the NBA players go through as far as like, going through school and like getting drafted. There's a draft for women's, yeah. Don't they have to do like the same things pretty much to get to? It's the same thing theoretically. But as far as the physical requirements, as far as the level of skill required, as far as the level of strength, speed, agility, it's not no way the same. That's why nobody knows when the WNBA draft is. So you think if the physical requirements and the skill requirements changed as far as the WNBA goes, that they would get more attendance at their games? One of the suggestions, actually Tracy McGrady, I think he made this suggestion to a WNBA player. And this is part of the issue. He was like, have you guys considered maybe lowering the rims to 9 feet? What are the rims at now? 10. It's the same as men's rims. And his point was if you lower the rims to 9 feet, y'all could dunk now, y'all could do more. It's more of an exciting game, this and that. And she was insulted. She was like, no, I've played on the 10 foot room all my life and I'm not lowering it and we're not, and how dare you and this and that. So it's like, the average woman is not going to be able to jump as high as the average man. The average elite woman is not going to be able to jump as high. Is there a study that says that? That's just biology. I mean, do you think they could?   She can't get, what, does that have to do with anything? I think she could do it if she wants to do it. Okay, let's talk about it. It's like the man practices and she's in the gym like she's supposed to be. I don't think her, you know, woman has anything to do with it, whether she can get up there or not. So men and women are equal, physically? Yes, but no. Explain. Yes, but no. In that sense and talking about sports, I don't think it's right to say, oh, we got to make, you know, these exceptions because you're women. That's like the comparison I see in my mind is seeing like a disabled person, for instance, and assuming that they need your help. They don't, they didn't ask for your help. So why are you just assuming that you need to make this, you know, exception for them or, you know. Yeah, but the disabled Olympic sprinter world record shouldn't be the same as you're saying both. Like, they should have a different world record based on their, you know, capabilities. Abilities, yeah. I don't know if that's the same for, I don't know. And the idea is women can't, on average, women cannot run as fast as men. On average, women are not as strong as men. On average, women aren't as agile and physically whatever is men. So the requirement should be lower. Do you think they should be the same as men? Again, I'm not a sports person. So like my sports opinion is just like, hmm. But a lot of people who have these opinions aren't sports people and that's why they have them. I know my lane. I know I do not know sports, but if those women and those people that participate in women's basketball wanted to be the same, I think it should be the same. But you, but then you can't also think they should get paid the same. Because if you think they should get paid the same my question would be where is the money coming from?  I don't know adjusting as far as like who they draft adjusting. No, they're drafting the best. They're drafting the best and you're saying the best is still like not as good as the best men. Actually, they actually did what's funny. They did the Americans women's soccer team, which is the best soccer team. We female soccer team in the world. They did a scrimmage against a high school boys team in like Australia. They lost 7-0. Could have been a bad day. I do know that about sports, you know. 7-0 though. Or those boys could have been training for like three years ahead of time because they really wanted to be there. You're not here when I'm saying the national team versus 15 year olds. I'm not gonna say that. No, the boys are 15. 15-60, they beat them by 7-0. So I mean at some point we're gonna have to acknowledge they ate it. What were the conditions? Was it raining outside? No, it was sunny day. We're gonna have to admit it. We're just gonna have to admit it. Was it a home game? Was it a big game? The national team the World Cup winning American women's team was beaten by some guys. I'm just gonna bow down to it was a bad day for them. It's a bad day. Maybe they want to make the little boys feel good. 7-0? You know what? I don't know much about soccer. Okay, I'll put it in context. 7-0 in soccer is like getting beat 120 to 0 in basketball. Hmm, okay. It's bad. Okay. Yeah, like 7-0 is like Brazil. Like the elite elite team. Why is it so hard for them to admit like men are physically superior? Why is that so hard? Let's talk about it. Why is that hard? I mean, I guess for me personally I come from a family of a lot of women and a lot of very like strong independent women who have always went above and beyond to you know do for themselves and not really rely on anyone and so I don't know I just haven't been taught to like, oh, he's a man. He's superior. Like that's just physically. No, I don't think men are superior. I think men are physically superior. In any way though. But why is that hard to admit? Because you can try to pick up something and I'm going to at least try to pick up that same thing that you just picked up. I'm not going to say I'm a woman. I can't pick that up. Like, no. I'm going to try to pick that up. Absolutely. I think you should but you know what I think is the issue. What's the issue? I'm not willing to on a person to person level not even men or women but I think more specifically men or women if I'm not willing to acknowledge your strengths I can't fully appreciate you. Because there's the sense of anything I could do or anything you could do I could do better. And unfortunately I think one of the consequences of feminism is it creates an environment where most women, particularly our women have no appreciation for men to the point where you can't even admit that we are physically superior. Like at least admit that. You can try to pick the thing up. I don't like the word superior. I think women are emotionally empathetically superior. You guys are better nurturers just off top. And I'm not saying some men aren't great teachers nurses, caretakers but the average woman is superior to the average man in that regard. And as a consequence of my testosterone I'm going to have denser bone structure I'm going to have more musculature than the average woman. So my thing is why can't we admit that? Do we need a minute? Do men go out of their way to say you're just emotionally superior? I think they should. But do they? I think they should. Shouldn't do are different though. Part of the reason they don't is number one I don't think enough men are taught to but number two in that battle it's hard to say you got that. I don't want to admit defeat. I'm the type of person I'm going to say this is where you're better but on the flip side you should be able to admit you can open a jar of pickles better than I can. Okay but to go back to what you just said if men cannot admit where women have strengths that they don't why do women have to oh we have to step into that we have to admit that you guys are superior but you guys aren't able to you know what I'm saying? No I think both sides should admit. Yeah both sides have to it can't just be like a woman less you know just make sure not like I will say this though I will say and we about to get controversial in a second I will say the consequences I think the consequences of women not admitting it outweigh the consequences of men not admitting it simply because one of the things that's coming out of the transgender movement is the idea that trans women are women so trans women should be in women's spaces whether it's sports whether it's spas whether it's you know spaces that have been exclusively reserved for women and because you're unwilling to recognize that physically biologically that is not a woman you subject yourself to whatever harm is a consequence of that you want to give examples? Okay I'm listening there is a there was a UFC fighter by the name of Fallon Fox Fallon Fox transition at the age of like 30 from a man to a woman so puberty had already happened this and that identifies as a woman fights in the UFC was a terrible fighter but was biologically a man okay the consequence of that was he was breaking women's skulls okay so damage that wouldn't have otherwise happened if you were fighting a fellow woman you have a high school wrestler who was breaking women's records and dominating the wrestling circuit because biologically he was a man or you have other instances cyclist power lifters this and that so is that fair to women? is it fair? you've been training to sprint all your life you got to run against Usain Bolt with a wig on you can't say it like that now okay is it fair? hmm that's interesting I don't know