256 Views

Download Presentation
##### Chapter 3.3 CPCTC and Circles

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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 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**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**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 Theorem 19 C A This means that L L**Sample Problem Using CPCTC**Statement Reason Given: ; Prove:**Sample Problem With Circles**Given: N Prove: Statement Reason Q M O N NN L P As simple as this!! R**Sample Problem With Both Ideas**Statement Reason D B C E A Given: C Prove:**Extra Problems**Statement Reason W Y Z X Given: ; Prove: V**...More**Statement Reason R M P O Given: C ; Prove:**And More!**Statement Reason A B D C Given: B Prove:**!**! ! And Even More!! ! ! Given: M = 3x+5 =6x-4 Find: x ! M N ! L !**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.**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!