Geometry

Question Analysis

This question is about applying the Triangle AA (Angle - Angle) Similarity Postulate. The key is to check if two pairs of corresponding angles in and are congruent to determine if the triangles are similar.

 

Key Concept Explanation

The AA Similarity Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This is because the sum of the interior angles of a triangle is . So, when two pairs of angles are congruent, the third pair must also be congruent, which means the triangles have the same shape (but not necessarily the same size).

 

Step - by - Step Solution

1. Identify the congruent angles:

We are given that (marked angles).

Also, and are vertical angles. Since vertical angles are congruent,

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