Geometry

Question Analysis

This question focuses on identifying the median of a triangle. The key is to correctly apply the definition of a median, which is a line segment connecting a vertex to the mid - point of the opposite side, while distinguishing it from other types of line segments like perpendicular bisectors and angle bisectors.

 

Key Concept Explanation

A median of a triangle is a line segment that joins a vertex of the triangle to the mid - point of the opposite side.

 

Step - by - Step Solution

1. Recall the definition of a median.

2. Analyze each option:

For : The arc markings indicate that is an angle bisector. There is no indication that is the mid - point of the opposite side, so does not meet the criteria of a median.

For : Although is the mid - point of , the fact that makes it a perpendicular bisector, not a median. A median only requires connection to the mid - point, not perpendicularity.

For : is a point on , not the mid - point of the side opposite