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
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)

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
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 

4. 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).