[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]
[color=#000000]Suppose the [/color][color=#9900ff]entire purple median[/color] [color=#000000]of the triangle above measures[/color] [color=#9900ff]18 inches[/color]. [color=#000000]What would the distance[/color] [color=#9900ff][i]BG[/i] [/color][color=#000000]be? What would the distance[/color] [i][color=#9900ff]GF[/color][/i] [color=#000000]be? [/color]
[color=#000000]Suppose the[/color] [color=#1e84cc]entire blue median[/color] [color=#000000]of the triangle above measures[/color] [color=#1e84cc]12 inches[/color]. [color=#000000]What would the distance[/color] [i][color=#1e84cc]AG [/color][/i][color=#000000]be? What would the distance [/color][i][color=#1e84cc]GE[/color][/i] [color=#000000]be?[/color]
What is the exact value of the ratio AG/GE? [br][br]What is the exact value of the ratio CG/GD? [br][br]What is the exact value of the ratio BG/GF?
What do you notice about your results for (3) above?
[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]