1. Chapter 3.3 CPCTC and Circles
Megan O’Donnell 9
5/30/08

2. Objectives
After studying this section you will be able to understand the following:
The principle of CPCTC
The basic properties of circles

3. CPCTC
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent C P T

4. CPCTC Explained In the diagram Therefore, we must draw
the conclusion that
This is because the
angles are corresponding
parts of congruent triangles,
meaning they are exact replicas
of each other. R D N I G O

5. 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. M
Circle M

6. Radii of Circles
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 is called a radius. L E

7. Theorem 19 Theorem 19 states that all radii of a circle are
This means that L L

8. Sample Problem Using CPCTC
Statement Reason 1.
1.Given 2.
2.Given 3.
3. If then 4.
4. Vertical angles are 5.
5. AAS (1,3,4) 6.
6. CPCTC
Given: ;
Prove:

9. Sample Problem With Circles
Given: N
Prove:
Statement Reason Q N
1.Given 2.
2.All radii of
a are M O N NN L P
As simple as
this!! R

10. Sample Problem With Both Ideas
Statement Reason C
1. Given 2.
2.All radii of a
are 3.
3.Vertical angles
Are 4.
4.SAS (2,3,2) 5.
5. CPCTC D B C E A
Given: C
Prove:

11. Extra Problems
Statement Reason 1. 2. 3. 4. W Y Z X
Given: ;
Prove: V

12. ...More 1. 2. 3. 4. 5. 6. 7. 8. Statement Reason R M P O Given: C ;
Prove:

13. And More!
Statement Reason 1. 2. 3. 4. 5. 6. A B D C
Given: B
Prove:

14. ! ! !
And Even More!! ! !
Given: M
= 3x+5
=6x-4
Find: x ! M N ! L !

15. Answers 1. 1.Given 2. 2.Given 3. 3.Reflexive 4. 4.CPCTC 1. C 1.Given
Right s
Lines form right 4.
4.Rt s are 5.
5.All radii of a
are 6.
6.Reflexive 7.
7.SAS (4,5,6) 8.
8.CPCTC

16. And more Answers 1. C 1.Given 2. 2.Given 3. 3.All radii of a 4.
Statement Reason C
1.Given 2.
2.Given 3.
3.All radii of a
Are 4.
4.Reflexive 5.
5.SSS (2,3,4) 6.
6.CPCTC
3x+5=6x-4
9=3x
X=3
We can set these segments equal to each other because they are radii. We learned that all radii of a circle are congruent.

17. Works Cited
Fogiel, Matthew. Problem Solvers Geometry. Piscataway: Research and Education System, 2004.
Milauskas, George, Richard Rhoad, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston: McDougal Littell,1991.

18. The end!
YAY GEOMETRY!