1. Successful Proof Plans
Questions to be asked to create successful proofs to show that
two triangles are congruent

2. Questions 1. What is given? 2. What is implied?
3. Do we have enough information to prove that 3 parts of 2 triangles are congruent?

3. Successful Proof Plans
What 3 elements do we need to prove that 2 triangles are congruent?
Angle-Angle-Side (AAS)
Angle-Side-Angle (ASA)
Side-Angle-Side (SAS)
Side-Side-Side (SSS)

4. Example A B C D
GIVEN: AB CD
AB = CD
PROVE: CBA = BDC

5. SOLUTION 1. WHAT IS GIVEN? 2 SIDES ARE CONGRUENT AND PARALLEL.
2. WHAT IS IMPLIED?
ANGLES ABC AND BCD ARE CONGRUENT DUE
TO ALTERNATE INTERIOR ANGLES.
SIDE BC IS CONGRUENT TO ITSELF DUE TO
REFLEXIVE PROPERTY.

6. SOLUTION 3. DO WE HAVE ENOUGH INFORMATION TO PROVE
THAT TWO TRIANGLES ARE CONGRUENT?
YES, SINCE WE HAVE 2 PAIRS OF SIDES, AND
1 PAIR OF ANGLES CONGRUENT.
CONCLUSION: SAS