# G.GCI.3 Medians and Centroid Dance

- Author:
- Dan Dale, Tim Brzezinski

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.## 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 ratio AG/AE? What is the exact value of the ratio CG/CD? What is the exact value of the ratio BG/BF?

## 5.

What do you notice about your results for (4) above?

## 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.