Warm upGiven: SM Congruent PM <SMW Congruent <PMWProve: SW Congruent WP

1. SM Congruent PM 1. Given2. <SMW Congruent <PMW 2. Given3. MW Congruent MW 3.

Reflexive4. ΔSMW Congruent ΔPMW 4. SAS5. SW Congruent WF 5.

CPCTC

WARM UP

NW = SW Given<MNS = <TSN Given<3 = <4 Given<MNW = <TSW Subtraction<1 = < 2 Vertical <s are =Δ MNW = Δ TSW ASAMN = TS CPCTC

3.3 CPCTC and Circles

CPCTC: Corresponding Parts of Congruent Triangles are Congruent.

Matching angles and sides of respective triangles.

P

M

SW

Given: SM = PM<SMW = <PMW

Prove: SW = WPP

M

SW

~~

~

Statement Reason

1. SM = PM 1. Given

2. <SMW = <PMW 2. Given

3. MW = MW 3. Reflexive property

4. ΔSMW = ΔPMW 4. SAS (1, 2, 3)

5. SW = PW 5. CPCTC

~~

~

~

~

• Circles: By definition, every point on a circle is equal distance from its center point.

• The center is not an element of the circle.

• The circle consists of only the rim.

• A circle is named by its center.

• Circle A or A

• A

•

Given: points A,B & C lie on Circle P.PA is a radiusPA, PB and PC are radii

Area of a circle Circumference A = Лr2 C = 2ЛrWe will usually leave in terms of piPi = 3.14 or 22/7 for quick calculationsFor accuracy, use the pi key on your calculator

T 19: All radii of a circle are congruent.

Given: Circle O<T comp. <MOT<S comp. <POS

Prove: MO = PO~

R

T

P

OK

M

S