Geometry Final Proof Review
1. Given:
A
 BAC   ACD
 BCA   DAC
 EDA   ABC
B
Prove: ABCD is a rectangle
E
D
C
C
2. Given: CD
m
m
 ABC is isosceles, with base AB
Prove:  DAB   DBA
D
A
B
B
3. Given: AE is an altitude
D
E
FD is an altitude
ABDC is a parallelogram
F
Prove: BF  EC
A
C
A
B
4. Given: AE  EB
DE  EC
Prove:
 ACD   BDC
E
D
C
5. Given:  A
AC is an altitude
a
A
Prove: AC is a median
B
6. Given: ACEG is a rectangle
B, D, F & H are midpoints
A
C
D
C
B
H
D
Prove: BHFD is a parallelogram
G
E
F
A
7. Given:  O, BO is an altitude
O
Prove: AB  CB
B
C
A
 ED
CD  ED
<AEF  <CDF
C
8. Given: AE
F
Prove: AD  EC
E
D
A
9. Given:
 ACE is isosceles with base CE
B, D, F are midpoints
Prove:
B
F
 ABD   AFD
C
D
E
S
1 is complementary to 4
2 is complementary to 3
RT bisects  SRV
Prove:  S   V
10. Given:
R
3
4
1
2
T
V
A
 ABC is isosceles with base BC
BF  CG , FH  BC , GI  BC
 OFG   OGF
Prove:  HFO   IGO
11. Given:
F
B
A
12. Given: Diagram as shown
1  4
Prove:
2  3
R
1
2
G
H
O
I
T
3
S
4
C
K
13. Given: OP  RS
KO  KS
M is the midpoint of OK
T is the midpoint of KS
M
T
Prove: MP  TR
O
Prove:
 WRS is isosceles
R
P
14. Given: PR  ST
NP  VT
P  T
P
S
T
W
N
S
R
V
B
Z
X
15. Given:
 XYZ is isosceles with base YZ
A, B trisect YZ
Prove: XA  XB
Y
16. Given: P is the midpoint of XZ
1  2
Prove: XY  YZ
A
Z
1
W
P
2
X
Y
A
17. Given: AF || EC
AF  EC
BE  FD
D
F
E
Prove: ABCD is a parallelogram
B
C