Lesson 5: 4-5: Proving Right Triangles Congruent

1. What theorems about triangle congruence have you already learned that could help develop theorems about the special case of right triangles?
2. What properties of right triangles can help determine if two right triangles are congruent?

G.CO.10
Prove theorems about triangles
G.SRT.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

https://docs.google.com/document/d/1Wi6oBP9pbwdBW1CPr4x4vVBOYkSXVKTdszWiPd1Ccm4/copy?usp=sharing

The right triangle congruence theorems LL, HA, and LA are related to other postulates and theorems about triangle congruence. LL is a special case of the SAS Postulate, HA is a special case of the AAS Theorem, and LA is a special case of the ASA Postulate. The HL Theorem is unique to right triangles since SSA is not sufficient to prove non-right triangles congruent.

Many structures like bridges have support beams in the shape of triangles. Making sure the angles and lengths are correct is critical to the integrity of the structure.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections to the special case of right triangles by being able to explain why it's necessary to state that the two triangles are right in order to prove the triangles are congruent by LL.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.