Honors Geometry
Chapter 3 Quiz Review Question Answers
1.
What does CPCTC stand for?
Corresponding Parts of Congruent Triangles are Congruent!!
2.
State the SAS congruence postulate
If two sides and and included angle in one triangle are congruent to the corresponding
sides and angle in another triangle, then the triangles are congruent.
3.
CN ≅ WN
∠C ≅ ∠W
C
Yes!!
Is RN ≅ ON ?
CNR ≅
Why?
W
N
WNO by ASA
R
⇒ RN ≅ ON because Corresponding Parts of
Congruent Triangles are Congruent ( CPCTC) .
O
4.
H is the midpoint of GJ
I
G
∠G ≅ ∠I
Is KH ≅ HI ?
NO!! This Cannot Be Determined ( CBD) !!
Why?
The congruent parts do not correspond
H
K
J
5.
Is ∠O ≅ ∠R?
F
∴
FUO ≅
FUR by SSS
⇒ ∠O ≅ ∠R by CPCTC
U
O
Baroody
R
Page 1 of 4
Honors Geometry
Chapter 3 Quiz Review Question Answers
6.
BT ≅ EU
BU ≅ ET
B
E
Is ∠E ≅ ∠B ?
∴
BUT ≅
R
ETU by SSS
⇒ ∠E ≅ ∠B by CPCTC
U
T
B
E
U
T
U
T
7.
Given:
Prove:
A
BA ≅ BF; FC ≅ AE
AB ⊥ CD
∠1 ≅ ∠2
∠BAC ≅ ∠BDE
2
E
1
F C
Statements
1. Given
2. FC ≅ AE
2. Given
4. AB ⊥ CD
5. ∠CBA & ∠EBD are right ∠s
A 6. ∠CBA ≅ ∠EBD
7. ∠1 ≅ ∠2
8. ∠AEB & ∠FCB are straight ∠s
9. ∠1 is supp. to ∠BCA
10. ∠2 is supp. to ∠BED
A 11. ∠BCA ≅ ∠BED
12.
BAC ≅ BDE
13. ∠BAC ≅ ∠BDE
Baroody
D
G
Reasons
1. BA ≅ BF
S 3. CB ≅ EB
B
3. Subtraction Property of ≅ Segments
4. Given
5.
6.
7.
8.
9.
10.
11.
12.
13.
Definition of ⊥ Segments
RAT
Given
Assumed from diagram
If ∠s form a straight ∠, they are supplementary
Same as 9
Supplements of ≅ ∠s are ≅
ASA ( 6, 3, 11)
CPCTC
Page 2 of 4
Honors Geometry
Chapter 3 Quiz Review Question Answers
8.
Given:
A
CD ≅ EF
BD ≅ AE
∠GDC ≅ ∠GEF
Prove:
G
∠ACE ≅ ∠BFD
C
D
Statements
E
F
Reasons
1. CD ≅ EF
S 2.
3.
4.
5.
6.
A 7.
B
1. Given
CE ≅ FD
∠GDC ≅ ∠GEF
∠CDE & ∠DEF are straight ∠s
∠GDC & ∠GDE are supplementary
∠GEF & ∠GED are supplementary
∠GDE ≅ ∠GED
Addition Property of ≅ Segments
Given
Assumed from diagram
If 2 ∠s form a straight ∠, they are supplementary
Same as 5
Supplements of ≅ ∠s are ≅
8. Given
9. SAS ( 2, 7, 8)
10. CPCTC
2.
3.
4.
5.
6.
7.
S 8. BD ≅ AE
9. ACE ≅ BFD
10. ∠ACE ≅ ∠BFD
9.
A
Given:
B
CD ≅ EF
∠GDC ≅ ∠GEF
AC ⊥ CF; BF ⊥ CF
Prove:
G
AE ≅ BD
C
D
E
Statements
S
A
1. Given
2.
3.
4.
5.
6.
7.
2.
3.
4.
5.
6.
7.
Addition Property of ≅ Segments
Given
Assumed from diagram
If 2 ∠s form a straight ∠, they are supplementary
Same as 5
Supplements of ≅ ∠s are ≅
8.
9.
10.
11.
12.
Given
Definition of ⊥
RAT
ASA (7, 2, 10)
CPCTC
CE ≅ FD
∠GDC ≅ ∠GEF
∠CDE & ∠DEF are straight ∠s
∠GDC & ∠GDE are supplementary
∠GEF & ∠GED are supplementary
∠GDE ≅ ∠GED
9. ∠ACE & ∠BFC are right ∠s
10. ∠ACE ≅ ∠BFC
11. ACE ≅ BFD
12. AE ≅ BD
Baroody
Reasons
1. CD ≅ EF
8. AC ⊥ CF; BF ⊥ CF
A
F
Page 3 of 4
Honors Geometry
Chapter 3 Quiz Review Question Answers
10.
Given:
Prove:
O
IO ≅ OZ
IU ≅ZH
C & L are midpoints
∠1 ≅ ∠2
C
∠ICH ≅ ∠ZLU
L
1
N
2
I
U
Statements
1. IO ≅ OZ
2. C & L are midpoints
S 3. IC ≅ ZL
4. IU ≅ ZH
S 5. IH ≅ ZU
6. ∠1 ≅ ∠2
7. ∠NIU & ∠EZH are straight ∠s
8. ∠1 is supp. to ∠CIH
9. ∠2 is supp. to ∠LZU
A 10. ∠CIH ≅ ∠LZU
11. CIH ≅ LZU
12. ∠ICH ≅ ∠ZLU
Baroody
H
Z
E
Reasons
1. Given
2. Given
3. Division Property of ≅ Segments
4. Given
5.
6.
7.
8.
9.
10.
11.
12.
Addition Property of ≅ Segments
Given
Assumed from diagram
If ∠s form a straight ∠, they are supplementary
Same as 9
Supplements of ≅ ∠s are ≅
SAS (3, 11, 6)
CPCTC
Page 4 of 4