Download Vocabulary - Hartland High School

Section 5.3 Use Angle Bisectors of Triangles
Goal  Use angle bisectors to find distance relationships.
TERM
MEANING
Angle Bisector
Ray, line, or segment that divides
an angle into two congruent
adjacent angles
PICTURE
PS is the
angle bisector
of QPR
The distance
Distance from a point to a line
Length of the perpendicular
segment from the point to the line
from S to PQ
is SQ because SQ  PQ
O
Incenter
Concurrency of angle bisectors of
a triangle
QS = QR = QT
R
S
Q
N
T
ANGLE BISECTOR THEOREM
If a point is on the bisector of an angle,
then it is equidistant from the two sides
of the angle.
CONVERSE OF THE ANGLE BISECTOR
THEOREM
If a point is on the interior of an angle and is
equidistant from the sides of the angle, then
it lies on the bisector of the angle.
If AD bisects BAC and
DB  AB and DB  AC ,
If DB  AB and DB  AC
and DB = DC, then
Then DB = DC
Example 1: Use the Angle Bisector Theorem
a. Find the measure of CBE.
AD bisects BAC
b. Find the measure of LM .
Example 2: Find the value of x that would make P lie on the bisector of J ?
P
Section 5.3 Use Angle Bisectors of Triangles
Example 3: In the diagram, V is the incenter of ΔPQR. Find VS.
Checkpoint
1. Find the value of x.
2. Find the value of x.
3. In the diagram, L is the incenter of ΔFGJ. Find LK.