Geometry

Question Analysis

The main focus of this question is to complete the proportion using the properties of similar triangles. It requires identifying the similar triangles in the diagram and applying the concept of equal ratios of corresponding sides. This tests understanding of geometric similarity and the ability to correctly match corresponding sides in similar triangles.

 

Key Concept Explanation

If two triangles are similar, the ratios of their corresponding side lengths are equal. In this case, since and is common to both and (by the angle - angle similarity criterion),  . For similar triangles, if we have sides in one triangle and in the other, then .

 

Step - by - Step Solution

1. Identify the similar triangles:

Given that and is common, we can conclude that by the AA (angle - angle) similarity criterion.

2. Set up the proportion for corresponding sides:

We know that is one ratio of corresponding sides. The side