16.4 Proving Congruent Triangles: Hypotenuse-Leg Theorem

In this lesson I will teach you the Hypotenuse-Leg theorem for proving triangles congruent. This is a nice special case theorem for congruent triangles. As the name implies, we can prove two triangles congruent if they have hypotenuses (longest leg of a triangle) and another corresponding side congruent. Now, what makes the HL theorem a special case theorem is it only applies to triangles that are RIGHT- i.e. one of the angles is 90 degrees. Assuming you have watched all the other lessons in this chapter you know we have many theorems to prove triangles congruent. Just a quick review these theorems are the SSS, SAS, ASA, AAS and now finally the HL theorem. Don't think any one method or theorem is better than another. You need to master all the congruent triangle theorems as it will give you more problem solving "tools" in geometry. Please continue to focus on taking well organized notes and practice is a must. Quick question: could you easily identify all the postulates and theorems you have learned in the course so far? If not be smart and get your notes organized the effort will pay off.


  1. Watch The Lesson Video First - Take Good Notes.

Practice Problems:

16.4 GeoCongruentTrianglesHLThmPreview.pdf