Geometry

Question Analysis

This question focuses on applying the SAS (Side - Angle - Side) Triangle Similarity Theorem. The main task is to check if the ratios of the corresponding sides that include the equal angles are equal. We need to correctly identify the corresponding sides and the included angles in both triangles and then calculate and compare the side - length ratios.

 

Key Concept Explanation

The SAS Triangle Similarity Theorem states that 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. In this case, we need to verify if the sides including the equal  angles in  and  are proportional.

 

Step - by - Step Solution

1. Identify the sides including the equal 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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