Geometry

Question Analysis

This question focuses on determining the nature of line segment in a triangle given the equality of two angles, testing knowledge of angle bisectors, mid - segments, and perpendicular bisectors.

Key Concept Explanation

Angle bisector: A line segment that divides an angle of a triangle into two equal - measure angles.

Mid - segment: A line segment that connects the midpoints of two sides of a triangle.

Perpendicular bisector: A line that is perpendicular to and bisects a side of a triangle.

Step - by - Step Solution

1. Given that .

2. By the definition of an angle bisector, since divides into two equal - measure angles, is an angle bisector.

Option Analysis

A.Angle bisector: Correct. As