GEOMETRY Worksheet

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GEOMETRY Worksheet
≅∆s Worksheet II
NAME___________________________________
DATE______________________ PERIOD______
Write ∆ congruence (if possible) and tell which postulate (SSS, SAS, ASA, or AAS) you are using.
1. ∆GKM≅∆__________ by __________
2. ∆ABC≅∆__________ by __________
G
GK  ML
GK≅ML
K
M
L
4. ∆KLG≅∆__________ by __________
P
G
GL bisects KM
GL bisects ∠KGM
S
R
E
C
B
3. ∆PRQ≅∆__________ by __________
R is midpoint of
both PT and QS
D
A
B ≅ E
C is midpoint of BE
∠DCB≅∠ECA
Q
T
K
5. ∆RNG≅∆__________ by __________
L
6. ∆DAB≅∆__________ by __________
N
RN ≅ NE
∠R ≅ ∠E
A
AB  DC
∠A ≅ ∠C
A
D
E
7. ∆WIT≅∆__________ by __________
W
T is midpt. of HI
WI  HC
B
G
S
R
M
C
8. ∆CON≅∆__________ by __________
CO ≅ GC
ON ≅ NG
I
T
O
C
N
G
C
H
9. ∆GEO≅∆__________ by __________
10. ∆TES ≅∆__________ by __________
OG bisects ∠EOM
EO ≅ MO
E is midpoint of both
TA and SX
TS ≅ AX
E
G
O
T
E
X
S
M
A
3
11. ∆DEB≅∆__________ by __________
12. ∆KEG≅∆__________ by __________
C
DE ≅ EC
BE ≅ AE
D
E is midpoint of KW
∠KEG ≅ ∠WEH G
∠K ≅ ∠W
E
H
B
K
A
13. ∆TVU≅∆__________ by __________
W
14. ∆MDB ≅∆__________ by __________
T
∠VTU ≅ ∠UVW
∠ TVU ≅ ∠UWV
E
V
D is midpoint of MT
BD ≅ ZT
BD  ZT
U
Z
B
M
D
T
W
15. ∆WUY≅∆__________ by __________
16. ∆BAD≅∆__________ by __________
V
U is midpoint of both
YX and WV
WY ≅ VX
AD bisects ∠BAC
BA ≅ CA
X
U
C
D
A
B
W
Y
17. ∆PFS≅∆__________ by __________
18. ∆AED≅∆__________ by __________
P
FP ≅ HP
RF ≅ SH
R
S
F
19. ∆COL≅∆__________ by __________
∆COU≅∆__________ by __________
A
L
D
AB  DC
AD  BC
B
U
C
F
20. ∆ABD≅∆__________ by __________
C
O
B
E
D
H
∠CUD ≅ ∠CLO
CU≅CL
∠OCU≅∠DCL
A
AE ≅ FC
DE ≅ FB
∠BED ≅ ∠DFB
D
4
C
5
Geometry
Worksheet-Congruent Triangles III
Name___________________________________
Date_________________________Period______
Label the drawing with the given information and state why the triangles are congruent. Use all eight
theorems (SSS, SAS, ASA, AAS, HA, HL, LL, LA)
1. ∆POR ≅ ∆_________ by ________
∠POR ≅ ∠TOR
PO ≅ TO
P
2. ∆LFE ≅ ∆_________ by ________
LF is the ⊥ bisector of ET
O
R
T
L
E
F
3. ∆PNO ≅ ∆_________ by ________
4. ∆HOM ≅ ∆_________ by ________
N is the midpoint of OE
P
PN ≅ HE
HM bisects ∠OHE
∠O ≅ ∠E
H
T
H
PO ⊥ ON
HN ⊥ NE
O
O
E
E
N
M
5. ∆MIT ≅ ∆_________ by ________
6. ∆RUJ ≅ ∆_________ by ________
I ≅ E
JR⊥ UY
JR bisects ∠UJY
J
TI  ME
T
I
E
M
U
R
7. ∆XTE ≅ ∆_________ by ________
8. ∆NEW ≅ ∆_________ by ________
X is the midpoint of
both TS and AE
NW ⊥ NE
SW ⊥ SE
∠NEW ≅ ∠SEW
T
A
E
W
X
E
N
S
6
Y
S
9. ∆PTC ≅ ∆_________ by ________
∠T ≅ ∠I
∠TPC ≅ ∠PCI
10. ∆TUH ≅ ∆_________ by ________
P
H
HU bisects ∠OHT
UH bisects ∠OUT
I
O
T
T
C
U
11. ∆MAO ≅ ∆_________ by ________
12. ∆NOC ≅ ∆_________ by ________
MA ⊥ OA
A is the midpoint of MR
O
C
CO ≅ NE
CN ≅ OE
M
O
A
N
E
R
13. ∆ULP ≅ ∆_________ by ________
PL bisects ∠UPA
LP bisects ∠ALU
P
14. ∆HRO ≅ ∆_________ by ________
A
U
L
15. ∆DGI ≅ ∆_________ by ________
DG ≅ ER
NE ≅ IG
DG ⊥ NI
RE ⊥ NI
D
M
O
E
16. ∆ANY ≅ ∆_________ by ________
I
E
G
N
H
HR ⊥ RE
ME ⊥ ER
O is the midpoint
of RE
∆HMO is isos.
with base HM
R
R
YA ⊥ AK
SK ⊥ KA
N is the midpoint
of YS
Y
A
K
N
S
7
Geometry
Proofs using Isosceles Triangles
1. Given:
Prove:
Name__________________________________
Date______________________Period_______
∠3 ≅ ∠4
MA ≅ MC
M
3 1
A
4
C
2
C
2. Given:
Prove:
∆CAN is an isosceles triangle with vertex ∠N
CA || BE
∆NEB is an isosceles triangle.
1
2
B 3
E
4
N
G
F
3. Given:
Prove:
5
∠5 ≅ ∠6
FR ≅ GS
∠4 ≅ ∠3
3
4
1
X
6
2
R
S
B
4. Given:
Prove:
∠3 ≅ ∠4
∠1 ≅ ∠2
∆ABC is isosceles with base AC
1 2
E
3
A
4
C
C
5. Given:
Prove:
CA ≅ CB
∠1 ≅ ∠2
AQ ≅ BP
1
A
8
P
2
Q
B
A
Geometry Pre AP
CPCTC Proofs Worksheet I
CPCTC: Corresponding Parts of Congruent Triangles are Congruent
Use one of the congruence theorems we have studied (SSS, SAS, AAS, ASA) to prove that the triangle
are congruent. Then use CPCTC to help draw further conclusions. Your answers should be in flow proof
format.
B
1.
Given: BD ⊥ AC
D is the midpoint of AC
Prove: ∠A ≅ ∠C
A
C
D
E
G
Given: ∠E ≅ ∠P
K is the midpoint of EP
Prove: EG ≅ MP
2.
K
P
M
3.
R
T
Given: RT  WQ
∠R ≅ ∠Q
Prove: RW ≅ TQ
Q
W
B
4.
Given: ∠A ≅ ∠C
∠1 ≅ ∠2
Prove: BD bisects ∠ADC
1 2
A
C
3 4
D
5.
E
G
Given: H is the midpoint of GM
H is the midpoint of EK
Prove: EG  MK
H
M
K
9
Geometry Pre AP
CPCTC Proofs Worksheet II
Use one of the congruence theorems we have studied (SSS, SAS, ASA, AAS, HA, HL, LL, LA) to prove that the
triangle are congruent. Then use CPCTC to help draw further conclusions. Your answers should be in flow proof
A
format.
1.
Given:
Prove:
CA≅RA
CS≅RS
∠ CHR≅ ∠ RIC
H
I
S
1
2
C
2.
R
Given: WR ≅ ST
WT ≅ SR
Prove: WT  SR
R
W
T
3.
S
Given: AB  EG
B
A
C
AB ≅ EG
∠A ≅ ∠G
Prove: AD ≅ GC
D
G
E
H
4.
K
Given: ∠H ≅ ∠W
P is the midpoint of HW
Prove: HW bisects KQ
P
Q
5.
6.
W
B
Given: AB ≅ BC
∠A ≅ ∠C
Prove: ∠AEB ≅ ∠CDB
E
D
A
Given: QP ⊥ PT
C
Q
ST ⊥ PT
QP ≅ ST
∠Q ≅ ∠S
S
M
Prove: M is the midpoint of PT
10
P
T

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