Geometry

Question Analysis

This question is about applying the Triangle Angle Bisector Theorem. Since  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 line segment bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides. In , with  bisecting , we can set up a proportion between the segments of side  (  and ) and sides  and .

 

Step - by - Step Solution

1. Recall the Triangle Angle Bisector Theorem formula: For  with angle bisector , we have .

This is because the theorem dictates that the ratio of the two segments of the side opposite the bisected angle () is equal to the ratio of the other two sides of the triangle ( and ).

 

Option Analysis

A.: Incorrect. The theorem does not involve the angle - bisecting segment

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