1. 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

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

3. Using Congruent Triangles: 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
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
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 S
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
<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
<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!