Chapter 3.3 CPCTC and Circles

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 C T C

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. 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. The Basics of Circles 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 Theorem 19 C A This means that L L

8. Sample Problem Using CPCTC Statement Reason Given: ; Prove:

9. Sample Problem With Circles Given: N Prove: Statement Reason Q M O N NN L P As simple as this!! R

10. Sample Problem With Both Ideas Statement Reason D B C E A Given: C Prove:

11. Extra Problems Statement Reason W Y Z X Given: ; Prove: V

12. ...More Statement Reason R M P O Given: C ; Prove:

13. And More! Statement Reason A B D C Given: B Prove:

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

15. Answers

16. And more Answers Statement Reason 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!