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  and  are vertical angles (and thus equal), we can focus on checking the ratios of the corresponding sides that include this angle (for SAS) or consider other criteria if applicable.

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 vertical angles:

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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