Angle Bisector

A segment that cuts an angle in A segment that cuts an angle in halfhalf

B

A

CD

1 2

In ABD, AC bisects BAD. If m 1 = 41

find m 2.

G

F

H

I

In FHI, IG is an angle bisector. Find m . HIG

5 1( )x ( )4 1x

Point of Concurrency

Incenter - The point of concurrency formed by the intersection of the three bisectors of a 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.

F

D

E

P

CA

B

2

The angle bisectors of triangle TUV meet at point W.

Find the value of d

F

Y

E

4d - 1

VT

U

W

2d + 7

Median

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

Median

Vertex

Point of ConcurrencyCentroid – The point of concurrency formed by the intersection of the three medians of a triangle

CentroidThe 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.

A

B

M

P E

C

N

If AN = 12, find AE.

In ABC, AN, BP, and CM are medians.

A

B

M

P E

C

N

If CE = 16, find EM.

In ABC, AN, BP, and CM are medians.

A

B

M

P E

C

N

If EP = 3, find EB and BP.

Special Segments in the Coordinate Plane