Exercise 3 Page 351

Let's think about perpendicular bisectors and angle bisectors individually.

Perpendicular Bisectors

From Exploration 1, we saw a variety of observations regarding the perpendicular bisectors. Here are the two major observations.

1. They always cross forming a point of intersection.
2. This point of intersection is always equidistant from the vertices of the triangle.

Conjecture: The point where the three perpendicular bisectors intersect is always equidistant from the vertices of the triangle.

Angle Bisectors

From Exploration 2, we saw a variety of observations regarding the angle bisectors. Here are the main ones.

1. They always cross forming a point of intersection.
2. This point of intersection is always equidistant from the sides of the triangle.

Conjecture: The point where the three angle bisectors intersect is always equidistant from the sides of the triangle.