Download CPCTC – Corresponding Parts of Congruent Triangles are Congruent.

G.CO.B.8 STUDENT NOTES & PRACTICE WS #4 – geometrycommoncore.com
1
In objective G.CO.B.7 we discussed how if two triangles are congruent to each other there are a number of
other things that we know – that the corresponding angles and sides are also congruent. In the proofs below
we you might notice that the ‘PROVE’ item is not to prove two triangles congruent…. It is to prove two
corresponding pieces (angles or sides) to be congruent. The general strategy will be to first prove triangles to
be congruent so that we can make a statement about sides or angles also being congruent. We often use the
abbreviation CPCTC as a reason for stating corresponding sides or angle to be congruent – it stands for:
CPCTC – Corresponding Parts of Congruent Triangles are Congruent.

ABC  DEF
A congruence statement for triangles
relates one identical object to another by
identifying the corresponding parts that
match each other.
AB  DE
A   D
BC  EF
B   E
CA  FD
C  F
Prove the following relationships.
GIVEN:
AB || DE & BC  DC
PROVE:
AC  EC
GIVEN:
AC  EC &
B
A
E
C
D
STATEMENT
1. AB || DE
2. BC  DC
3. B  D
4. A  E
5. ABC  EDC
6. AC  EC
REASON
1. Given
2. Given
3. ||  Alt. Int.  
4. ||  Alt. Int.  
5. AAS
6. CPCTC 
BC  DC
PROVE:
 B  D
STATEMENT
1. AC  EC
2. BC  DC
3. BCA  DCE
4. BCA  DCE
5. B  D
E
B
C
A
D
REASON
1. Given
2. Given
3. Vertical  
4. SAS
5. CPCTC 
G.CO.B.8 STUDENT NOTES & PRACTICE WS #4 – geometrycommoncore.com
NYTS (Now You Try Some)
Prove the following relationships.
1. GIVEN:
B
AC bisects DAB
A
& AB  AD
C
PROVE:
D
 B  D
STATEMENT
REASON
1. Given
1. AC bisects DAB
2. AB  AD
2. Given
3. BAC  DAC
3. Def.  Bisector
4. AC  AC
5. ABC  ADC
6. B  D
4. Reflexive Prop.
5. SAS
6. CPCTC 
2. GIVEN:
C is the midpoint of AE
& BD
PROVE:
 AB  DE
STATEMENT
1. C is the midpoint of
AE & BD
2. AC  EC
3. BC  DC
4. BCA  DCE
5. ABC  EDC
6. AB  DE
2
B
A
E
C
D
REASON
1. Given
2. Def. of Midpoint
3. Def. of Midpoint
4. Vertical  
5. SAS
6. CPCTC 