Transcript 4.4 Using Congruent Triangles: CPCTC

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

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*
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-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-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!