Special Line through Triangle V1 (Theorem Discovery)

Interact with the following applet for a few minutes. As you do, be sure to change the locations of the triangle's vertices each time before (and even after) sliding the slider. Then, answer the questions that follow.

1.

How would you describe the FIRST small white point that appeared as you animated the diagram?

2.

What can you conclude about the gray line and the gray side of the triangle? Why can you conclude this?

3.

What can you conclude about a line that passes through the midpoint of one side of a triangle and is parallel to another side of the triangle?

4.

Suppose you know that a line that passes through the midpoint of one side of a triangle and is parallel to another side of the triangle. Write a formal argument that proves this line MUST pass through the midpoint of the 3rd side of the triangle.