Geometry

Question Analysis

The main focus is to correctly identify the definition of a median of a triangle among the given options.

Key Concept Explanation

A median of a triangle is a line segment that has one endpoint at a vertex of the triangle and the other endpoint at the mid - point of the opposite side. This concept is fundamental in understanding the properties and centers related to triangles, such as the centroid which is formed by the intersection of the three medians.

Step - by - Step Solution

1. Analyze each option:

A: "A middle of the triangle."

This description is too vague. It doesn't precisely define what a median is. A median is a specific type of line segment, not just an abstract "middle" of the triangle. So, this option is incorrect.

B: "A segment that connects two midpoints of two sides."

A segment that connects two midpoints of two sides is called a midsegment, not a median. So, this option is incorrect.

C: "A segment that connects the vertex and the opposite side at 90 degrees."

A segment that connects a vertex and the opposite side at a 90 - degree angle is an altitude, not a median. So, this option is incorrect.

D: "A segment with endpoints at the vertex and midpoint of the opposite side."<...