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)

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.

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).