HW

Finish 5.
1 Practice & pg. 304 (1

4, 12

14)
www.westex.org
HS, Teacher Website
1
2

12

11
Warm up
—
Geometry CPA
T
he two triangles
must be congruent. W
rite
the congruence statement and
name the
postulate or theorem
.
&
GOAL:
I will be able to:
1. p
rove and apply theorems about perpendicular
bisectors.
2. p
rove and apply theorems about angle
bisectors
.
HW

Finish 5.1 Practice & pg. 304 (1

4, 1
2

14)
www.westex.org
HS, Teacher Website
N
ame _________________________
Date ________
Geometry
CPA
5

1 Perpendicular and Angle Bisectors
When a point is the same distance from two or more
objects, the p
oint is said to be
__________________
from
the objects. Triangle congruence theorems can be
used to prove
theorems about equidistant points.
A
__________
is a set of points that satisfies a given condition. The perpendicular bisector
of a seg
ment can be defined as the locus of points in a plane that are equidistant from the
endpoints of the segment.
Example 1: Applying the Perpendicular Bisector Theorem and Its Converse
a.
Find
MN.
B. Find BC.
C. Find TU.
YOU TRY:
Given that
DE
= 20.8,
DG
= 36.4, and
EG
=36.4, find
EF
.
Remember that the distance between a point and a line is the length of the perpendicular
segment from the point to the line.
Based on these theorems, an angle bisector can be defined as th
e locus of all points in the
interior of the angle that are
__________________
from the sides of the angle.
Example 2: Applying the Angle Bisector Theorem
a. Find BC.
b
. Find m
EFH
, given
that m
EFG
= 50°.
YOU TRY:
a.
Find m
MKL
.
b.
Given that m
WYZ
= 63°,
XW
= 5.7,
and
ZW
= 5.7, find m
XYZ
.
Example 3: Writing Equations of Bisectors in the Coordinate Plane
Write an equation in point

slope form for the perpendicular bisector of the segment with
endpoints
C
(6,
–
5) and
D
(10, 1).
YOU TRY:
Write an equation in point

slope form for the perpendicular bisector of the segment with
endpoints
P
(5, 2) and
Q
(1,
–
4).
5

1 Practice
Use the diagram for Items 1
–
2.
1.
Given that m
ABD
= 16°, find m
ABC
.
2.
Given that
m
ABD
= (2
x
+ 12)° and m
CBD
=
(6
x
–
18)°, find m
ABC
.
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