# Medians of a Triangle

## Median

A median of a triangle is the segment from the midpoint of a side of the triangle to the opposite vertex.

## Constructing Medians

In the applet above: 1) Use the geometry tools to find the midpoint of each side. 2) Use the geometry tools to make the segment from each midpoint to the opposite vertex. 3) Label any point(s) of intersection.

## Medians

What do you notice about the medians? Manipulate the triangle by moving the vertices around. What do you notice?

## Centroid

The point of concurrency for the medians of a triangle is called the centroid.

## Properties of the Centroid

Use the distance tool to find the length of AF, AG, GF.

What do you notice about the three lengths? Find the measures of BE, BG, and GE. Find the measures of CD, CG, and GD. What do you notice? What conclusions can you make?

## Hint

If you are stuck and cannot find a relationship. Try dividing the lengths.

## Centroid Theorem

For any triangle, the distance from a vertex to the centroid is two - thirds the length of that median.