Angle Bisectors of Triangles
- Author:
- Lee Carroll
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.