3.3 cpctc and circles objective: after studying this lesson you will be able to apply the principle...

3.3 CPCTC and Circles3.3 CPCTC and Circles

Objective: After studying this lesson you will be able to apply the principle of CPCTC and recognize

some basic properties of circles.

AA

CCTT

CPCTCCPCTC

““CCorresponding orresponding PParts of arts of CCongruent ongruent TTriangles are riangles are CCongruent”ongruent”

OO

DDGG

Suppose that . Can we say that ?

After we have proven two triangles are congruent we will use

as a reason. Corresponding parts refer to the matching angles and sides in the respective triangles.

DOG CAT D C

Point O is the center of the circle shown below.

Definition of a circle: every point of the circle is the same distance from the center.

OO

The center is not a part of the circle, just the outside or the “rim”. Circles are named by their centers.The circle above is named circle O or O

PPAA

BBCC

Points A, B, and C lie on circle P. PA is called the radius

PA, PB, and PC are called radii.

Formulas to remember!2

2A rC r

Theorem: all radii are congruent

Given:

Prove: AB CD

Statement Reason

DD

BB

CC

AA

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

P PP

Given:

Prove:

is complementary to T MOT

MO PO

Statement Reason

1.

2.

3.

4.

5.

6.

7.

8.

1.

2.

3.

4.

5.

6.

7.

8.

O

RR

SS

TT

KKOO PP

MM is complementary to S POS

Summary:Summary:When is it appropriate to When is it appropriate to use CPCTC as a reason in use CPCTC as a reason in a proof?a proof?

Homework: worksheetHomework: worksheet