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4.4 - Using
Congruent
Triangles:
CPCTC
Chapter 4
Congruent Triangles
Goals / “I can…”
• Use triangle congruence and CPCTS to prove parts
of 2 triangles are congruent
C.P.C.T.C.
•
•
•
•
•
C orresponding
P arts (of)
C ongruent
T riangles (are)
C ongruent
If two triangles are congruent, then their
corresponding parts are also congruent.
*You must prove that the triangles are congruent
before you can use CPCTC*
http://www.lz95.org/lzhs/Math/knerroth/geometry/Geometry%20Chap%203%20PDF/3.3-CPCTC.ppt#256,1,CPCTC
Using CPCTC
Given: ∠ ABD = ∠ CBD, ∠ ADB = ∠ CDB
Prove: AB = CB
B
A
C
D
∠ ABD = ∠ CBD, ∠ ADB = ∠ CDB
BD = BD
∆ABD = ∆CBD
AB = CB
Given
Reflexive Property
ASA (Angle-Side-Angle)
CPCTC (Corresponding Parts of Congruent
Triangles are Congruent)
Using CPCTC
Given: MO = RE, ME = RO
Prove: ∠ M = ∠ R
O
M
MO = RE, ME = RO
OE = OE
∆MEO = ∆ROE
∠M=∠R
R
E
Given
Reflexive Property
SSS (Side-Side-Side)
CPCTC (Corresponding Parts of Congruent
Triangles are Congruent)
Using CPCTC
Given: SP = OP, ∠ SPT = ∠ OPT
Prove: ∠ S = ∠ O
S
T
P
SP = OP, ∠ SPT = ∠ OPT
PT = PT
∆SPT = ∆OPT
∠S=∠O
Given
Reflexive Property
SAS (Side-Angle-Side)
CPCTC (Corresponding Parts of Congruent
Triangles are Congruent)
O
Using CPCTC
Given: KN = LN, PN = MN
Prove: KP = LM
K
L
N
P
KN = LN, PN = MN
∠ KNP = ∠ LNM
∆KNP = ∆LNM
KP = LM
M
Given
Vertical Angles
SAS (Side-Angle-Side)
CPCTC (Corresponding Parts of Congruent
Triangles are Congruent)
Using CPCTC
Given: ∠ C = ∠ R, ∠ T = ∠ P, TY = PY
Prove: CT = RP
C
R
Y
T
∠ C = ∠ R, ∠ T = ∠ P,
TY = PY
Given
∆TCY = ∆PRY
AAS (Angle-Angle-Side)
CT = RP
CPCTC (Corresponding Parts of
Congruent Triangles are Congruent)
P
Using CPCTC
Given: AT = RM, AT II RM
Prove: ∠ AMT = ∠ RTM
A
M
AT = RM, AT || RM
∠ ATM = ∠ RMT
TM = TM
∆TMA = ∆MTR
∠ AMT = ∠ RTM
T
R
Given
Alternate Interior Angles
Reflexive Property
SAS (Side-Angle-Side)
CPCTC (Corresponding Parts of
Congruent Triangles are Congruent)