Geometry

Question Analysis

This question focuses on applying the Triangle Angle Bisector Theorem. Given that  is the angle bisector of  in , we need to determine the correct proportion among the given options.

 

Key Concept Explanation

The Triangle Angle Bisector Theorem states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides. In , since  bisects , the segments of side  (  and ) are proportional to sides  and .

 

Step - by - Step Solution

1. Analyze each option based on the Triangle Angle Bisector Theorem:

For the option , cross - multiplying gives

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