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

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?

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)

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

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.

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