Triangle Within a Triangle: An Investigation
Move the slider to view the formation of a triangle within another triangle using trisection of the original triangle's sides.
Then answer the following questions.
Observe triangle within triangle . 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. Make a conjecture about the ratio of the area of to the area of .
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 all triangles? Explain your reasoning. (Feel free to move around the vertices of in the animation above.)