Angle Bisectors & Medians

Angle Bisector A segment that cuts an angle in half

A 1 2 D B C

F I G H

The Incenter Always lies Inside the Triangle Point of Concurrency Incenter - The point of concurrency formed by the intersection of the three bisectors of a triangle. The Incenter Always lies Inside the Triangle

Incenter It is the same distance from each side of the triangle to the incenter.

The angle bisectors of the triangle meet at point P. Find PF.

The angle bisectors of triangle TUV meet at point W. Find the value of d U 2d + 7 Y W F T V E 4d - 1

Median Median Vertex A segment from the vertex of a triangle to the midpoint of the opposite side.

The centroid always lies Point of Concurrency Centroid – The point of concurrency formed by the intersection of the three medians of a triangle The centroid always lies inside the triangle

Centroid The centroid is two-thirds of the distance from each vertex to the midpoint of the opposite side.

In ABC, AN, BP, and CM are medians. If AN = 12, find AE. A B M P E C N

In ABC, AN, BP, and CM are medians. If CE = 16, find EM. A B M P E C N

In ABC, AN, BP, and CM are medians. If EP = 3, find EB and BP. A B M P E C N

Special Segments in the Coordinate Plane