Geometry

Question Analysis

This question involves applying the Converse of the Side - Splitter Theorem. The main goal is to determine whether the line  is parallel to  by checking if the sides of  are divided proportionally by .

 

Key Concept Explanation

The Converse of the Side - Splitter Theorem states that if a line divides two sides of a triangle proportionally, then the line is parallel to the third side. In , we need to check if . We can find  and .

 

Step - by - Step Solution

1. Calculate the lengths of  and :

Given  and , then .

Given

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