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. Since  is a common angle, we can focus on checking the ratios of the corresponding sides that include this angle (for SAS) or look at angle - angle relationships (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. Identify the sides including the common angle :

In , the sides including  are  and .

In , the sides including  are  and .

2. Calculate the ratios of the corresponding sides:

Calculate

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