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 Objectives: Prove 2 right triangles are  using HL Throrem 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 Tent Design. Show the two triangles are congruent, so you would only have to make one pattern to construct the tent flaps. Given: Prove: Given Def of perp bisector Def of Rt ∆s Def of Isosceles HL Theorem Reflexive Prop of 

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).