Geometry

Question Analysis

This question is about determining if  and  are similar using the AA (Angle - Angle), SSS (Side - Side - Side), and SAS (Side - Angle - Side) Triangle Similarity Theorems. We have one pair of equal angles (), and we can check side - length ratios for SAS or find another pair of equal angles for AA.

Key Concept Explanation

AA (Angle - Angle) Similarity Theorem: If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

SSS (Side - Side - Side) Similarity Theorem: If the ratios of the lengths of the three pairs of corresponding sides of two triangles are equal, then the two triangles are similar.

SAS (Side - Angle - Side) Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Step - by - Step Solution

1. Check for SAS similarity:

Identify the sides including the equal angle. In , the sides including  are  and . In , the sides including  are  and

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