G.CO.B.8 GUIDED PRACTICE WS #4 – geometrycommoncore.com
1
What can we conclude if we know two triangles are congruent?
Answer: That corresponding sides are congruent and that corresponding angles are congruent.
What does CPCTC mean?
Answer: Corresponding Parts of Congruent Triangles are Congruent.
How do the ‘PROVE’ statements differ from the previous worksheet? What do you think we have to do to
prove these sides and angles to be congruent?
Answer: First prove the triangles are congruent…. And then their corresponding parts will be congruent.
Prove the following relationships.
1. GIVEN:
AB || DE & BC  DC
PROVE:
AC  EC
STATEMENT
1. AB || DE
2. BC  DC
3. B  D
4. A  E
5. ABC  EDC
6. AC  EC
3. GIVEN:
AC bisects DAB
& AB  AD
B
A
E
C
D
REASON
STATEMENT
1. AC  EC
1. Given
2. Given
3. ||  Alt. Int.  
2. BC  DC
3. BCA  DCE
4. ||  Alt. Int.  
5. AAS
4. BCA  DCE
5. B  D
E
B
C
A
D
REASON
1. Given
2. Given
3. Vertical  
4. SAS
5. CPCTC 
6. CPCTC 
4. GIVEN:
B
A
PROVE:
 B  D
STATEMENT
1. AC bisects DAB
2. AB  AD
2. GIVEN:
AC  EC &
BC  DC
PROVE:
 B  D
C
D
REASON
1. Given
2. Given
3. BAC  DAC
4. AC  AC
3. Def.  Bisector
4. Reflexive Prop.
5. ABC  ADC
6. B  D
5. SAS
6. CPCTC 
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
B
A
E
C
D
REASON
1. Given
2. Def. of Midpoint
3. Def. of Midpoint
4. Vertical  
5. SAS
6. CPCTC 