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 (), so we'll check the ratios of the corresponding sides that include this angle to see if the SAS criterion is met.

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 equal 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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