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Chapter 4 Congruent Triangles Ms. Olifer

Using Congruent Triangles: CPCTC Objective: - use triangle congruence and CPCTC to prove that parts of two triangles are congruent. Chapter 4 Congruent Triangles Ms. Olifer. Review: What congruence postulates and theorem do you know?. Postulates: SSS SAS ASA Theorem: AAS.

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Chapter 4 Congruent Triangles Ms. Olifer

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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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