Geometry

Question Analysis

This question is about applying the Side - splitter theorem corollary. Since in , we can set up a proportion using the segments of the sides divided by the parallel line to find the length of . The key is to correctly identify the corresponding segments.

 

Key Concept Explanation

The Side - splitter theorem corollary 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 with , we have . Also, .

 

Step - by - Step Solution

1. First, identify the known values:

, , and .

2. Set up the proportion according to the Side - splitter theorem corollary:

. Substitute the known values: .