1. Postulates and Theorems to show Congruence SSS: Side-Side-Side
Section 4-6 Congruence in Right Triangles (HL) SPI 32C: determine congruence or similarity between triangles SPI 32M: justify triangle congruence given a diagram
Postulates and Theorems to show Congruence
SSS: Side-Side-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle
AAS: Angle-Angle-Side
HL: Hypotenuse-Leg (right triangle only)

2. Hypotenuse-Leg (HL) Triangle Congruence
Theorem 4-6 Hypotenuse-Leg (HL) Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Right Triangles
Hypotenuse
To use the HL Theorem you must show the 3 conditions:
1. There are 2 right triangles
2. The triangles have congruent hypotenuses.
3. There is one pair of congruent legs.

3. Using HL Theorem for Right Triangles
Write a two–column proof.
Given: ABC and DCB are right angles, AC DB
Prove: ABC DCB
Statements Reasons
1. ABC and DCB are 1. Given right angles.
2. ABC and DCB are 2. Definition of a right triangle right triangles.
3. AC DB 3. Given
4. BC CB 4. Reflexive Property of Congruence
5. ABC DCB 5. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. (HL Theorem).