# Median and centroid of a triangle.

## Thm: median length of a ∆ and the length of the segments created by the centroid

Below is triangle ABC. Three red line segments are drawn from the vertices, points A, B & C, to the midpoints of the opposite sides, sides BC, AC & AB, respectively. These three line segments are called medians. The point ﻿(pt. G) where these medians intersect is called a centroid . The centroid divides a median into two segments of unequal length: a longer segment (AG) and a shorter segment (GD).

## Observe/Explore

If you move any of the vertices of ∆ABC, the length of the median, AD, will change, as will AG and GD. But there are specific relationships amongst the three lengths, AD, AG, and GD, that will not change try to discover what they are. ***FYI: at times the lengths generated by the applet can be off by a tenth. For example, BC, a side length, could be shown to be 12.9 when it should be 12.8 units.****

## MC

1. When a centroid divides a median into two segments, the ratio of the shorter segment's length to the longer segment's length will always be a______

Select all that apply
• A
• B
• C
• D
• E

## MC

2. When a centroid divides a median into two segments, the ratio of the median's length to shorter segment's length will always be a ______

Select all that apply
• A
• B
• C
• D
• E

## MC

3. When a centroid divides a median into two segments, the ratio of the longer segment's length to the median's length will always be ______

Select all that apply
• A
• B
• C
• D
• E

## fill-in

4. If the shorter segment of a median, created by the centroid, is 7.5 inches, then the longer segment is _____ inches.

## fill-in

5. If the longer segment of a median, created by the centroid, is 5/8 inches, then the shorter segment is _____ inches.

## fill-in

5. If a median of a ∆ is 12 inches long, then the shorter segment, created by the centroid, is _____ inches and the longer segment is ________ inches.