7.2 TWO PROOF-ORIENTED TRIANGLE THEOREMS

Objective:After studying this section, you will

be able to apply the no-choice theorem and the AAS theorem.

Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. (No-Choice Theorem)

A

B

C D

E

F

If there exists a correspondence between the vertices of two triangles such that two angles and a nonincluded side of one are congruent to the corresponding parts of the other, then the triangles are congruent. (AAS)

Theorem

Example 1

Given:

A

E

B

C

D

Prove:

DA CE

Example 2Given:

N O

T

P

S

Prove: NPRT is a rhombus

, ,

, ,

N R NTR P

TO NP TS PR

TO TS

R

Summary

Explain why if two right triangles have a pair of congruent acute angles, then the other pair of acute angles must be congruent.

Homework

Worksheet