3.3 CPCTC and Circles
Objective:
After studying this lesson you will be able to
apply the principle of CPCTC and recognize
some basic properties of circles.
A
O
C
D
T
G
Suppose that
DOG  CAT.
Can we say that
D  C ?
After we have proven two triangles are congruent we will use
CPCTC
“Corresponding Parts of Congruent
Triangles are Congruent”
as a reason. Corresponding parts refer to the matching angles and
sides in the respective triangles.
Point O is the center of the circle shown below.
O
Definition of a circle: every point of the circle is
the same distance from the center.
The center is not a part of the circle, just the
outside or the “rim”. Circles are named by their
centers.
The circle above is named circle O or
O
Points A, B, and C lie on circle P. PA is called
the radius
PA, PB, and PC are
A
called radii.
P
B
C
Formulas to remember!
A r
2
C  2 r
Theorem: all radii are congruent
D
C
Given:
P
P
A
Prove: AB  CD
Statement
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
B
Given: O
T is complementary to MOT
S is complementary to POS
K
O P
R
M
S
Prove: MO  PO
Statement
T
Reason
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8.
8.
Summary:
When is it appropriate to
use CPCTC as a reason in
a proof?
Homework: worksheet