Date:Topic: Proofs of Triangle Congruence (6.3)

Warm-up:List the angles from smallest to biggest

Can you make a triangle with sides 5 feet, 3 feet, and 2 feet? Why or why not?

The sum of the smallest two sides must be greater than the largest side: 3+2 = 5 3+2 is not greater than 5You cannot make a triangle with sides 5 feet, 3 feet, and 2 feet.

Proofs of Triangle CongruenceIn order to prove things we need evidence. We can use rules or theorems we already know to help us prove congruence.

Example:Given:

Prove:

1. , W C are Given

2. because vertical angles are congruent

3. #1 and #2 WPA CMA by Angle Side Angle (ASA)

Given:

Prove:

1. , RK ST Given

2. because shared sides are congruent

3. #1 and #2 RSK TKS by Side Side Side (SSS)

4. #3 R T because congruent triangles have all six pairs of congruent sides and angles.

R S

TK

RS KT

Given:

Prove:

1. BA YZ , bisects BA YBZ Given

2. #1 90 , 90m BAY m BAZperpendicular lines form 90° angles

3. #2 BAY BAZ both angles measure 90 degrees

4. #1 YBA ZBA angle bisector creates two equal angles

5. shared sides are equal

6. #3,#5 and #4 AYB AZB by Angle Side Angle (ASA)