Move the slider to view the formation of a triangle within another triangle using trisection of the original triangle's sides. [br][br]Then answer the following questions.
Observe triangle [math]\Delta DEF[/math] within triangle [math]\Delta ABC[/math]. How was the inner triangle formed? What do you wonder?
Now think about how the area of the inner triangle relates to the area of the outer triangle. [br][br]Make a conjecture about the ratio of the area of [math]\Delta DEF[/math] to the area of [math]\Delta ABC[/math].
Now view the following animation using the slider to reveal the relationship between the two triangles' areas.
Explain what is happening in the animation.
Are you still confident in your conjecture from Question 2?
Do you think this ratio is the same for [i]all[/i] triangles? Explain your reasoning. (Feel free to move around the vertices of [math]\Delta ABC[/math] in the animation above.)