5-1 Special Segments in Triangles

Objective: Use medians, angle bisectors, perpendicular bisectors and altitudes to solve problems.

RELEVENCE: Construction

Perpendicular Bisector of a Triangle

A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side.

Perpendicular Bisector

Median of a Triangle

A segment that joins a vertex of the triangle and the midpoint of the opposite side.

Median

Altitude of a Triangle

A segment from a vertex of the triangle to the line containing the opposite side and perpendicular to the line containing that side.

Altitude

Angle Bisector of a Triangle

A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint at another point on the triangle.

Angle Bisector

Example 1:

If SU is a median of ∆RST, find SR.

R

S

TU3x + 7 5x - 13

4x + 11

Example 2:

If GM is an angle bisector, find m∠IGM.

G H

I

M

(x + 12)°

m∠IGH = (3x – 5)°

Exit Ticket

Find BC if CD is a median of ∆ABC.

A B

C

D4x + 5 x + 20

3x + 8