Medians and Centroid Warm up Per 2

[color=#000000]Recall that a [/color][b][color=#980000]median of a triangle[/color] [/b][color=#000000]is a[/color][color=#980000] [b]segment that connects any vertex to the midpoint of the side opposite that vertex. [/b] [/color][color=#000000]Since a triangle has 3 vertices, it has 3 medians. [/color][br][br][color=#000000]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. [/color][br][br][color=#000000]Note: The[/color][color=#ff7700] [b]BIG ORANGE POINT[/b] [/color][color=#000000]that will appear is known as the[/color][color=#ff7700] [b]CENTROID[/b] [/color][color=#000000]of the triangle.[/color][br][br][i][color=#9900ff]Have fun with this![/color][/i] [color=#000000]Be sure to change the locations of the triangle's BIG WHITE VERTICES each time before re-sliding the slider. [/color]

1.What word can you use to describe the intersection of a triangle's 3 medians?

orthocenter centroid incenter circumcenter

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

9 12 6 18

2b. What would the distance GF be?

12 18 6

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

9 12 4 8

3b. What would the distance GE be?

4 8 9 12

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.

[color=#000000]Suppose you have a triangle with only 1 median drawn. Without constructing its other 2 medians, explain how you can locate the [/color][color=#ff7700][b]centroid[/b][/color] [color=#000000]of the triangle. [/color]