# 3.3 CPCTC and Circles ```Chapter 3.3 CPCTC and Circles
Megan O’Donnell
9
5/30/08
Objectives



After studying this section you will be able to
understand the following:
The principle of CPCTC
The basic properties of circles
CPCTC

CPCTC stands for
Corresponding Parts of
Congruent Triangles
are Congruent
C
P
C
T
C
CPCTC Explained
In the diagram RIN  DOG
Therefore, we must draw
the conclusion that R  D
This is because the
angles are corresponding
parts of congruent
triangles,
meaning they are exact
replicas
of each other.
R
N
D
I
G
O
The Basics of Circles

Point M is the center of
the circle shown to the
right. Circles are named
by their center point.
Thus, this circle is
called Circle M.
Circle M
M

L
E

In a circle’s definition
every point of the circle
is equidistant from the
center.
A line reaching from the
center to a point on the
outside of a circle, such
as LE is called a radius.
Theorem 19

Theorem 19 states that
all radii of a circle are 
Theorem 19
C
A
This means that CA  LA
L
L
Sample Problem Using CPCTC
Statement
Reason
1.
2.
A  D
1.Given
2  3
2.Given
3.
4.
BE  CE
3. If
5  6
then
4. Vertical
angles are

5. ABC  DCE 5. AAS (1,3,4)
6. AE  DE
6. CPCTC
Given: A  D ; 2  3
Prove: AE  DE
Sample Problem With Circles
Given:
N
Prove: QN  RN
Statement
1.
Reason
N
Q
1.Given
2.
QN  RN
a are 
As simple
as
this!!
M
L
NN
N
O
P
R
Sample Problem With Both Ideas
Statement
1.
2.
Reason
C
1. Given
CD  CE  CB  CA
3.BCA  DEC

are

3.Vertical angles
Are

4.BCA  DEC 4.SAS (2,3,2)
5. AB  DE
5. CPCTC
Given:
C
Prove: AB  DE
D
B
C
A
E
Extra Problems
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
Given: WX  WZ; VX
 VZ
Prove: WXV  WZV
W
Y
Z
X
V
...More
Statement
Reason
1.
2.
3.
1.
2.
3.
4.
5.
6.
4.
5.
6.
7.
8.
7.
8.
R
RO  MP
M
P
O
Given:
Prove:
C ; RO  MP
MR  PR
And More!
Statement
1.
Reason
1.
2.
2.
3.
3.
A
B
4.
4.
5.
5.
6.
6.
C
Given:
Prove: ABD  CBD
D
!
!
!
!
And Even More!!
!
Given:
!
LM
M
= 3x+5
MN =6x-4
M
N
Find: x
!
!
L
1. WX  WZ
2. VX  VZ
3. WV  WV
1.Given
2.Given
3.Reflexive
4. WXV  WZV 4.CPCTC
1.
C
1.Given
2. RO  MP 2.Given
3. ROM  ROP 3.  Lines form right
Right  s

4.ROM  ROP 4.Rt s are 
5.
MR  PR
are

6. RO  RO
6.Reflexive
ROM  ROP 7.SAS (4,5,6)
7.
8. MR  PR 8.CPCTC
Statement
1.
2.
3.
C
AB  CB
Reason
1.Given
2.Given
Are

4. BD  BD
4.Reflexive
5. ADB  CDB 5.SSS (2,3,4)
6.ABD  CBD 6.CPCTC
3x+5=6x-4
9=3x
X=3
We can set these
segments equal to each
other because they are
congruent.
Works Cited


Fogiel, Matthew. Problem Solvers Geometry.
Piscataway: Research and Education
System, 2004.