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CPCTC & Circles: Corresponding Parts of Congruent Triangles are Congruent

Explore the concept of CPCTC (Corresponding Parts of Congruent Triangles are Congruent) in the context of circles. Learn about the properties of circles and how to use them to prove congruence between corresponding parts of triangles.

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CPCTC & Circles: Corresponding Parts of Congruent Triangles are Congruent

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  1. CPCTC & Circles Lesson 3.3

  2. CPCTC: Corresponding Parts of Congruent Triangles are Congruent.

  3. M S P W Given: SM  PM <SMW  <PMWProve: SW  WP • Statement Reason • SM  PM 1. Given • <SMW  <PMW 2. Given • MW  MW 3. Reflexive property • ΔSMW ΔPMW 4. SAS (1, 2, 3) • SW  WF 5. CPCTC

  4. • 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 •

  5. 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

  6. Theorem 19: All radii of a circle are congruent. Given: Circle O <T comp. <MOT <S comp. <POS Prove: MO  PO T • Circle O • OT  OS • T is comp to MOT • S is comp to  POS • MOT  POS • T  S • MOT  POS • MO  PO • Given • All radii of a circle are . • Given • Given • Vertical angles are . • Complements of   s are . • ASA (5,2,6) • CPCTC P R K M O S

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