Geometry

Question Analysis

This question involves the Side - Splitter Theorem. The main focus is to use the proportional relationship created by a line parallel to one side of a triangle () to find the value of .

 

Key Concept Explanation

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. In , since , we have .

 

Step - by - Step Solution

1. First, identify the lengths of the segments:

We know that , , , and .

2. Set up the proportion according to the Side - Splitter Theorem:

.

3. Simplify the left - hand side of the proportion:

, so the proportion becomes .

4. Cross - multiply:

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