Geometry

Question Analysis

This question focuses on applying the Side - splitter theorem corollary. The key is to use the property of parallel lines in a triangle to determine the correct proportion between the sides of the triangles formed.

 

Key Concept Explanation

The Side - splitter theorem corollary states that when a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally.

 

Step - by - Step Solution

By the Side - splitter theorem corollary, the ratios of corresponding sides are equal. That is, .

 

Common Mistakes

Failing to correctly identify the corresponding sides of the similar triangles created by the parallel line.

Mixing up the order of the sides in the proportion, leading to incorrect ratios.

 

Summary

When a line is parallel to one side of a triangle and intersects the other two sides, the sides are divided proportionally. In this case, with

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