Activity: Medians and Centroid Dance
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.