7.2 Two Proof-Oriented Triangle theorems

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Presentation transcript:

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) B E C D F A

Theorem 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)

Example 1 A D Given: Prove: B E C

Example 2 Given: T R S Prove: NPRT is a rhombus P N O

Summary Homework Worksheet 7.2 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 7.2