CPCTC notes with answers.notebook
November 30, 2011
CPCTC ­ Corresponding Parts of Congruent Triangles are Congruent
B
A
D
ADB ≅
C
A C
ADB CBD
ABD BDC
AB DC
AD BC
DB DB
CBD by SSS
1
CPCTC notes with answers.notebook
November 30, 2011
Proofs with CPCTC:
Prove: corresponding parts are congruent
Ex) Prove: AB ≅CD
Write proofs exactly as we did before, but the second to last step is how the triangles are congruent, and the last step is what you are proving with a reason of CPCTC.
NOTE: You must prove triangles congruent before you can use CPCTC.
Prove: ∆PAR ≅ ∆PTR
Statements
Reasons
1. OM bisects LMN
LOM NOM
2. OM OM
3. LMO NMO
4. LMO NMO
5. ML MN
1. given
2. reflexive
3. definition of bisect
4. ASA
5. CPCTC
2
CPCTC notes with answers.notebook
Statements
1. DEG and DEF are right angles
EDG EDF
2. DE DE
3. DFE and DGE are right triangles
4. DFE DGE
5. FE EG
November 30, 2011
Reasons
1. given
2. reflexive
3. definition of right triangles
4. LA
5. CPCTC
X
Given: WX ≅ XY, XZ bisects WXY
1 2
Prove: 1 ≅ 2
Statements
W
Z
Y
Reasons
1. WX XY, XZ bisects 1. given
WXY
2. reflexive
2. XZ XZ
3. def. of bisect
3. WXZ ZXY
4. SAS
4. WXZ YXZ
5. CPCTC
5. WZ ZY
3