3.3 CPCTC and Circles

By: Josie LaCoe andSarah Parkinson

Period 1

CPCTC=

CorrespondingParts ofCongruentTriangles areCongruent

Explanation of CPCTC

If two triangles are congruent, then all of the corresponding parts of those two triangles are congruent.

Explanation of CPCTC

This means that if COW PIG, then and CO PI. This is also true for all other corresponding parts of the triangles.

PC

W

O

C P

I

G

Circles!!!

Point W is the center of this circle. All circles are named by their center, so this circle would be called circle W or O W.

.W

.

Circles!!!

A circle is made up of only the outer edge, not the center.

.WCircle (rim)

Center of circle (Not a part of the circle)

Circles!!!

Since all of points of a circle are the same distance from the center…

THEOREM 19!!!!-All radii of a circle are congruent!

Review Formulas

Although you probably know these formulas from previous math classes, here’s just a little refresher:

A= r C=2 r 2

3.141592654

Sample Problem #1

Given: OSProve: IE JO

Statements Reasons

1. OS 1. Given

2. SJ SO SI SE 2.All radii of a O are

3. JSO ISE 3. Vertical s are

4. JSO ISE 4. SAS (2,2,3)

5. IE JO 5. CPCTC

.

J

O

S

I

E

.

.

Solution:

Sample Problem #2

Given: OJFind the perimeter of SJP

Solution:SJ and PJ=1/2 PRSJ and PJ=1/2(12)SJ and PJ=6PS=7Perimeter of SJP=

6+6+7=19

7

12

S

JP

R

.

Practice Problem #1

Given: E A B is the mdpt of AE

Prove: C D

A

B

C

D E

Practice Problem #2

a. Find the coordinates of point Sb. Find the circumference of the circle

(Round to the nearest tenth)

.(107, 59)

.S

Practice Problem Solutions

1. Statements Reasons

1. E A 1. Given

2. B is mdpt of AE 2. Given

3. AB BE 3. Mdpt seg into 2 segs

4. ABC EBD 4. Vertical s are

5. ABC EBD 5. ASA (1, 3,4)

6. C D 6. CPCTC

Practice Problem Solutions

2a. The coordinates of the center of the circle is (107, 59) (107 being the x-coordinate and 59, the y-coordinate). This means the x-coordinate of S is 107 and since S is on the x-axis, the y-coordinate is 0, making the coordinates of S (107,0)

Practice Problem Solutions

2b. C=2 r C=2 59

C 370.7

Because the y-coordinate (the distance from the x-axis to the point) of the center of the circle is 59, this is also the radius of the circle (the distance from the center of a circle to the outside edge). This number is plugged into the equation and the equation is solved for C.

Works Cited

Rhoad Richard, George Milauskas, Robert Whipple. Geometry for Enjoyment and Challenge. Illinois: McDougal Littell, 1997. Print.