Using Congruent Triangles CPCTC Objective use triangle congruence

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 n Theorem: AAS n

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

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

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

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

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

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

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

Practice Time!