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10 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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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
.