# 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.