1. In the model below move the point in the center of the triangle around so it is equidistant from all three sides of the triangle.

a. Why are all of these distances measured along perpendicular lines?

b. How does this point seem to be related to the sides of the triangle?

2. Move the vertices of the triangle and perform the same task. How does the new location of this central point relate to the sides of the triangle?

3. Make a conjecture of how you can locate a point in a triangle that minimizes the sum of the distances to the three sides.

This point that is equidistant from the sides of the triangle is called the Incenter of a triangle.

4. Place a circle centered at the Incenter of the triangle going out to one vertex of the triangle. What do you notice about how this circle relates to the triangle? Will this always happen? Why?