Transcript 5-1 Special Segments in Triangles

5-1 Special Segments in Triangles
Objective: Use medians, angle
bisectors, perpendicular bisectors
and altitudes to solve problems.
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.
S
4x + 11
R 3x + 7 U 5x - 13
T
Example 2:
 If GM is an angle bisector, find m∠IGM.
I
M
G
(x + 12)°
m∠IGH = (3x – 5)°
H
Candy Ticket
 Find BC if CD is a median of ∆ABC.
C
3x + 8
A
4x + 5
D x + 20 B