# Medians & Centroid Dance

- Author:
- Cheris South, 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.**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.