# Medians & Centroid (A)

- Author:
- MsBuist, Tim Brzezinski

**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.

**Questions:**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? 5) What is the exact value of the ratio CG/CD? 6) What is the exact value of the ratio BG/BF? 7) What do you notice about your results for (4) - (7) above? 8) 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.

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? 5) What is the exact value of the ratio CG/CD? 6) What is the exact value of the ratio BG/BF?

7) What do you notice about your results for (4) - (7) above?

8) 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.