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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)