# Angle Bisectors of Triangles

## Given angle ABC. Use the geometry tools to construct the angle bisector. Label point D anywhere on the angle bisector.

## Angle Bisector

Use the geometry tools to find the angle measures of ABD and DBC. Move points A and C around. What do you notice about the angle measures?

## Angle Bisector

A segment or ray that cuts an angle into two equal parts.

## Incenter

If three or more lines intersect at a single point, then the lines are

**concurrent lines**The point where three or more lines intersect is called a**point of concurrency**. The point of concurrency for the angle bisectors of a triangle is called the**incenter**.## The angle bisectors for each angle of triangle ABC is given. Move the vertices to make different triangles.

## Angle Bisectors of Triangles

What do you notice about the incenter D? Use the distance measuring feature to find the distance from point D to each vertex. Manipulate the triangle one more time. What do you notice?

## The incenter D of triangle ABC is given. A segment perpendicular to each side through point D is also given.

## Incenter to Side distance

Use the distance tool to find DE, DF, and DG. Move the vertices to make different triangles. What do you notice?

## Incenter Theorem

The Incenter of any triangle is

**equidistant**to the sides of the triangle.