Chapter 3.3 CPCTC and Circles

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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 T

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

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

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

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

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:

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

Sample Problem With Both Ideas Statement Reason 1. 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:

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

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

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

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

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

And more Answers 1. C 1.Given 2. 2.Given 3. 3.All radii of a 4. Statement Reason 1. 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.

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.

The end! YAY GEOMETRY!