# Medians & Centroid Investigation

- Author:
- Stephanie Omobono, Tim Brzezinski

- Topic:
- Centroid or Barycenter

Recall that a

**median of a triangle**is a**segment that connects any vertex to the midpoint of the side opposite that vertex.**Since a triangle has 3 vertices, it has 3 medians. This applet will illustrate 2 very special properties about a triangle's 3 medians. Interact with it for a few minutes, then answer the questions that follow. Note: The**BIG ORANGE POINT**that will appear is known as the**CENTROID**of the triangle.*Have fun with this!*Be sure to change the locations of the triangle's BIG WHITE VERTICES each time before re-sliding the slider. After you have experimented, answer the questions below.1) What word can you use to describe the intersection of a triangle's 3 medians? How do they intersect?

2) Suppose the entire purple median of the triangle above measures 18 inches.
What would the distance *BG* be? What would the distance *GF* be?

3) Suppose the entire blue median of the triangle above measures 12 inches.
What would the distance *AG *be? What would the distance *GE* be?

4) What is the exact value of the following ratios? AG/AE = ? CG/CD = ? BG/BF = ? What do you notice when comparing them?

5) Suppose you have a triangle with only 1 median drawn. Without constructing its other 2 medians, explain how you can locate the **centroid** of the triangle.