Geometry

Question Analysis

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

 

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. Since the sum of interior angles in a triangle is , when two pairs of angles are congruent, the third pair must also be congruent, ensuring the triangles have the same shape (though not necessarily the same size).

 

Step - by - Step Solution

1. Find the third angle in :

Using the angle - sum property of a triangle (), in , . Given and , then

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