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Warm up. Given: SM Congruent PM <SMW Congruent <PMW Prove: SW Congruent WP. SM Congruent PM 1. Given <SMW Congruent <PMW 2. Given MW Congruent MW 3. Reflexive Δ SMW Congruent Δ PMW 4. SAS SW Congruent WF 5. CPCTC. WARM UP. NW = SW Given <MNS = <TSN Given <3 = <4 Given

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Warm up

Given: SM Congruent PM

<SMW Congruent <PMW

Prove: SW Congruent WP

  • SM Congruent PM 1. Given

  • <SMW Congruent <PMW 2. Given

  • MW Congruent MW 3. Reflexive

  • ΔSMW Congruent ΔPMW 4. SAS

  • 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 ASA

MN = TS CPCTC


M

P

S

W

3.3 CPCTC and Circles

CPCTC: Corresponding Parts of Congruent Triangles are Congruent.

Matching angles and sides of respective triangles.


Given sm pm smw pmw prove sw wp

M

P

S

W

Given: SM = PM <SMW = <PMWProve: SW = WP

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  • Statement Reason

  • SM = PM 1. Given

  • <SMW = <PMW 2. Given

  • MW = MW 3. Reflexive property

  • ΔSMW = ΔPMW 4. SAS (1, 2, 3)

  • SW = PW 5. CPCTC

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A

  • 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


Given points a b c lie on circle p pa is a radius pa pb and pc are radii
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 = 2Лr

  • We will usually leave in terms of pi

  • Pi = 3.14 or 22/7 for quick calculations

  • For accuracy, use the pi key on your calculator


T 19 all radii of a circle are congruent
T 19: All radii of a circle are congruent.

Given: Circle O

<T comp. <MOT

<S comp. <POS

Prove: MO = PO

T

P

R

K

M

O

S

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