Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Prove triangles similar using a valid criterion
Problem
\(\text{Two}~\text{pairs}~\text{of}~\text{corresponding}~\text{angles}\) in \(\text{two}~\text{triangles}\) are congruent. Name the similarity criterion this evidence satisfies and explain why side-length information is unnecessary.
Two corresponding angle pairs already determine a triangle’s shape. We’ll match the marked pairs, apply AA, use the triangle angle sum to explain why the third pair must also agree, and distinguish the resulting equal shape from the stronger claim of equal size.
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