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Mastering CPCTC in Congruent Triangles: A Practical Guide

Learn how to apply triangle congruence and CPCTC effectively to prove that parts of two triangles are congruent in this comprehensive guide. Explore congruence postulates like SSS, SAS, ASA, and the AAS theorem. Understand the significance of proving triangle congruence before utilizing CPCTC.

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Mastering CPCTC in Congruent Triangles: A Practical Guide

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  1. Using Congruent Triangles: CPCTCObjective:- use triangle congruence and CPCTC to prove that parts of two triangles are congruent. Chapter 4 Congruent Triangles Ms. Olifer

  2. Review: What congruence postulates and theorem do you know? • Postulates: SSS SAS ASA • Theorem: AAS

  3. Using Congruent Triangles: CPCTC • CPCTC: “Corresponding Parts of Congruent Triangles are Congruent” *You must prove that the triangles are congruent before you can use CPCTC*

  4. Using CPCTC Given: <ABD = <CBD, <ADB = <CDB Prove: AB = CB B A C <ABD = <CBD, <ADB = <CDB Given D BD = BD Reflexive Property ΔABD = ΔCBD ASA (Angle-Side-Angle) AB = CB CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  5. Using CPCTC Given: MO = RE, ME = RO Prove: <M = <R O R M E MO = RE, ME = RO Given OE = OE Reflexive Property ΔMEO = ΔROE SSS (Side-Side-Side) <M = < R CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  6. Using CPCTC Given: SP = OP, <SPT = <OPT Prove: <S = <O O T S SP = OP, <SPT = <OPT Given PT = PT Reflexive Property P ΔSPT = ΔOPT SAS (Side-Angle-Side) <S = <O CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  7. Using CPCTC Given: KN = LN, PN = MN Prove: KP = LM K L N KN = LN, PN = MN Given <KNP = <LNM Vertical Angles M P ΔKNP = ΔLNM SAS (Side-Angle-Side) KP = LM CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  8. Using CPCTC Given: <C = <R, <T = <P, TY = PY Prove: CT = RP C R Y <C = <R, <T = <P, TY = PY Given P T ΔTCY = ΔPRY AAS (Angle-Angle-Side) CT = RP CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  9. Using CPCTC Given: AT = RM, AT || RM Prove: <AMT = <RTM A T M R AT = RM, AT || RM Given <ATM = <RMT Alternate Interior Angles TM = TM Reflexive Property ΔTMA = ΔMTR SAS (Side-Angle-Side) <AMT = <RTM CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

  10. Practice Time!

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