Download Geometry M1: Unit 4 Practice Exam

Name: ________________________ Class: ___________________ Date: __________
Geometry M1: Unit 4 Practice Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which pair of triangles is congruent by ASA?
a.
b.
____
c.
d.
2. Name the theorem or postulate that lets you immediately conclude ABD  CBD.
a.
AAS
b.
SAS
c.
1
ASA
d.
none of these
ID: A
Name: ________________________
____
3. Can you use the SAS Postulate, the AAS Theorem, or both to prove the triangles congruent?
a.
b.
____
SAS only
AAS only
c.
d.
either SAS or AAS
neither
4. Based on the given information, what can you conclude, and why?
Given: H  L, HJ  JL
a.
b.
____
ID: A
HIJ  LKJ by ASA
HIJ  JLK by SAS
c.
d.
HIJ  JLK by ASA
HIJ  LKJ by SAS
5. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. mR  70,
mS  80, mF  70, mD  30, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell
which segment is congruent to RT .
a. yes, by ASA; FD
b. yes, by AAS; ED
c. yes, by SAS; ED
d. No, the two triangles are not congruent.
2
Name: ________________________
____
ID: A
6. Supply the missing reasons to complete the proof.
Given: A  D and AC  DC
Prove: BC  EC
Statement
1. A  D and
Reasons
1. Given
AC  DC
2. BCA  ECD
2. Vertical angles are congruent.
3. BCA  ECD
3.
?
4. BC  EC
4.
?
a.
b.
SAS; Corresp. parts of   are .
ASA; Corresp. parts of   are .
c.
d.
3
AAS; Corresp. parts of   are .
ASA; Substitution
Name: ________________________
____
ID: A
7. What is the missing reason in the proof?
Given: ABCD with diagonal BD
Prove: ABD  CDB
Statements
Reasons
1. Definition of parallelogram
1. AD  BC
2. ADB  CBD
3. AB  CD
4. ABD  CDB
5. DB  DB
6. ABD  CDB
a.
b.
____
2. Alternate Interior Angles Theorem
3. Definition of parallelogram
4. ?
5. Reflexive Property of Congruence
6. ASA
Alternate Interior Angles Theorem
ASA
c.
d.
Definition of parallelogram
Reflexive Property of Congruence
8. WXYZ is a parallelogram. Name an angle congruent to XWZ.
a.
XYW
b.
XYZ
c.
4
WYZ
d.
WXY
Name: ________________________
____
ID: A
9. Justify the last two steps of the proof.
Given: AB  DC and AC  DB
Prove: ABC  DCB
Proof:
1. AB  DC
2. AC  DB
3. BC  CB
4. ABC  DCB
a.
b.
1. Given
2. Given
3. ?
4. ?
Symmetric Property of  ; SAS
Reflexive Property of  ; SAS
c.
d.
Reflexive Property of  ; SSS
Symmetric Property of  ; SSS
____ 10. Name the angle included by the sides MP and PN .
a.
P
b.
N
c.
5
M
d.
none of these
Name: ________________________
ID: A
____ 11. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
a.
b.
AB AD
CBA  CDA
c.
d.
BAC  DAC
AB  AD
____ 12. State whether ABC and AED are congruent. Justify your answer.
a.
b.
c.
d.
yes, by either SSS or SAS
yes, by SAS only
yes, by SSS only
No; there is not enough information to conclude that the triangles are congruent.
____ 13. Which triangles are congruent by ASA?
a.
b.
VTU and HGF
none
c.
d.
6
VTU and ABC
ABC and TUV
Name: ________________________
ID: A
____ 14. Which two triangles are congruent by ASA?
MR bisects QO, and MQP  ROP.
a.
b.
none
MNP and ONP
c.
d.
MQP and MPN
MPQ and RPO
____ 15. What is the missing reason in the two-column proof?




Given: MO bisects PMN and OM bisects PON
Prove: PMO  NMO
Statements
Reasons


1. MO bisects PMN
2. PMO  NMO
3. MO  MO
1. Given
2. Definition of angle bisector
3. Reflexive property


4. OM bisects PON
5. POM  NOM
6. PMO  NMO
a.
b.
ASA Postulate
AAS Theorem
4. Given
5. Definition of angle bisector
6. ?
c.
d.
SAS Postulate
SSS Postulate
____ 16. YX is a perpendicular bisector to WZ at X between W and Z. ZWY  WZY. By which of the five
congruence statements, HL, AAS, ASA, SAS, and SSS, can you immediately conclude that WXY  ZXY?
a. HL, AAS, ASA, SAS, and SSS
c. HL and ASA
b. HL and AAS
d. HL, AAS, and ASA
7
Name: ________________________
ID: A
____ 17. Find the values of the variables in the parallelogram. The diagram is not to scale.
a.
b.
x  58, y  20, z  102
x  20, y  58, z  102
c.
d.
x  20, y  58, z  122
x  58, y  58, z  122
____ 18. In the parallelogram, mKLO  43 and mMLO  69. Find mKJM. The diagram is not to scale.
a.
112
b.
102
c.
43
d.
68
____ 19. In the parallelogram, mQRP  23 and mPRS  91. Find mPQR. The diagram is not to scale.
a.
114
b.
66
c.
8
91
d.
23
Name: ________________________
ID: A
____ 20. ABCD is a parallelogram. If mCDA  74, then mDAB 
a.
116
b.
148
c.
?
. The diagram is not to scale.
74
d.
106
____ 21. For the parallelogram, if m2  4x  26 and m4  3x  7, find m1. The diagram is not to scale.
a.
50
b.
140
c.
130
____ 22. ABCD is a parallelogram. If mBCD  108, then mDAB 
a.
82
b.
138
c.
d.
?
108
19
. The diagram is not to scale.
d.
72
____ 23. In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 2x – 4, and HE = 5y + 2. Find the values of x and y. The
diagram is not to scale.
a.
x = 9, y = 26
b.
x = 23, y = 8
c.
9
x = 26, y = 9
d.
x = 8, y = 23
Name: ________________________
ID: A
____ 24. Find AM in the parallelogram if PN =13 and AO = 4. The diagram is not to scale.
a.
13
b.
6.5
c.
8
d.
4
____ 25. LMNO is a parallelogram. If NM = x + 13 and OL = 2x + 7, find the value of x and then find NM and OL.
a.
b.
x = 6, NM = 19, OL = 19
x = 6, NM = 21, OL = 19
c.
d.
x = 8, NM = 21, OL = 21
x = 8, NM = 19, OL = 21
____ 26. In the figure, the horizontal lines are parallel and AB  BC  CD. Find JM. The diagram is not to scale.
a.
9
b.
12
c.
10
6
d.
3
Name: ________________________
ID: A
____ 27. In the figure, the horizontal lines are parallel and AB  BC  CD. Find KL and FG. The diagram is not to
scale.
a.
b.
KL = 7.3, FG = 7.3
KL = 7.7, FG = 7.7
c.
d.
11
KL = 7.7, FG = 7.3
KL  7.3, FG  7.7
ID: A
Geometry M1: Unit 4 Practice Exam
Answer Section
MULTIPLE CHOICE
1. ANS: C
PTS: 1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 1 Using ASA
KEY: ASA
DOK: DOK 1
2. ANS: C
PTS: 1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
KEY: ASA | AAS | SAS
DOK: DOK 2
3. ANS: B
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
KEY: ASA | AAS | reasoning
DOK: DOK 2
4. ANS: A
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 4 Determining Whether Triangles Are Congruent
KEY: ASA | reasoning
DOK: DOK 2
5. ANS: A
PTS: 1
DIF: L3
REF: 4-4 Using Corresponding Parts of Congruent Triangles
OBJ: 4-4.1 Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two
triangles are congruent
STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6
TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent
KEY: ASA | corresponding parts | word problem
DOK: DOK 2
6. ANS: B
PTS: 1
DIF: L3
REF: 4-4 Using Corresponding Parts of Congruent Triangles
OBJ: 4-4.1 Use triangle congruence and corresponding parts of congruent triangles to prove that parts of two
triangles are congruent
STA: MA.912.G.2.3| MA.912.G.4.4| MA.912.G.4.6
TOP: 4-4 Problem 1 Proving Parts of Triangles Congruent
KEY: ASA | corresponding parts | proof
DOK: DOK 2
7. ANS: A
PTS: 1
DIF: L3
REF: 6-2 Properties of Parallelograms
OBJ: 6-2.2 Use relationships among diagonals of parallelograms
STA: MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
TOP: 6-2 Problem 2 Using Properties of Parallelograms in a Proof
KEY: proof | two-column proof | parallelogram | diagonal
DOK: DOK 2
1
ID: A
8. ANS: B
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
OBJ: 6-2.1 Use relationships among sides and angles of parallelograms
STA: MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
TOP: 6-2 Problem 2 Using Properties of Parallelograms in a Proof
KEY: parallelogram | opposite angles
DOK: DOK 1
9. ANS: C
PTS: 1
DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates
STA: MA.912.G.4.3| MA.912.G.4.6
TOP: 4-2 Problem 1 Using SSS
KEY: SSS | reflexive property | proof
DOK: DOK 2
10. ANS: A
PTS: 1
DIF: L2
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates
STA: MA.912.G.4.3| MA.912.G.4.6
TOP: 4-2 Problem 2 Using SAS
KEY: angle
DOK: DOK 1
11. ANS: D
PTS: 1
DIF: L4
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates
STA: MA.912.G.4.3| MA.912.G.4.6
TOP: 4-2 Problem 2 Using SAS
KEY: SAS | reasoning
DOK: DOK 2
12. ANS: A
PTS: 1
DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
OBJ: 4-2.1 Prove two triangles congruent using the SSS and SAS Postulates
STA: MA.912.G.4.3| MA.912.G.4.6
TOP: 4-2 Problem 3 Identifying Congruent Triangles
KEY: SSS | SAS | reasoning
DOK: DOK 2
13. ANS: C
PTS: 1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 1 Using ASA
KEY: ASA
DOK: DOK 1
14. ANS: D
PTS: 1
DIF: L4
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 1 Using ASA
KEY: ASA | vertical angles
DOK: DOK 2
15. ANS: A
PTS: 1
DIF: L3
REF: 4-3 Triangle Congruence by ASA and AAS
OBJ: 4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
STA: MA.912.G.4.3| MA.912.G.4.6| MA.912.G.8.5
TOP: 4-3 Problem 2 Writing a Proof Using ASA
KEY: ASA | proof
DOK: DOK 2
16. ANS: B
PTS: 1
DIF: L3
REF: 4-6 Congruence in Right Triangles
OBJ: 4-6.1 Prove right triangles congruent using the Hypotenuse-Leg Theorem
STA: MA.912.G.2.3| MA.912.G.4.6| MA.912.G.5.4
TOP: 4-6 Problem 1 Using the HL Theorem
KEY: right triangle | HL Theorem | ASA | SAS | AAS | SSS | proof | word problem | problem solving |
reasoning
DOK: DOK 2
2
ID: A
17. ANS:
OBJ:
STA:
TOP:
KEY:
DOK:
18. ANS:
OBJ:
STA:
TOP:
DOK:
19. ANS:
OBJ:
STA:
TOP:
DOK:
20. ANS:
OBJ:
STA:
TOP:
DOK:
21. ANS:
OBJ:
STA:
TOP:
KEY:
DOK:
22. ANS:
OBJ:
STA:
TOP:
DOK:
23. ANS:
OBJ:
STA:
TOP:
KEY:
24. ANS:
OBJ:
STA:
TOP:
DOK:
25. ANS:
OBJ:
STA:
TOP:
DOK:
B
PTS: 1
DIF: L4
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
parallelogram | opposite angles | consecutive angles | transversal
DOK 2
A
PTS: 1
DIF: L4
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
KEY:
DOK 2
B
PTS: 1
DIF: L4
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
KEY:
DOK 2
D
PTS: 1
DIF: L2
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
KEY:
DOK 1
C
PTS: 1
DIF: L4
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
algebra | parallelogram | opposite angles | consecutive angles
DOK 2
C
PTS: 1
DIF: L2
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 1 Using Consecutive Angles
KEY:
DOK 1
B
PTS: 1
DIF: L3
REF:
6-2.2 Use relationships among diagonals of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 3 Using Algebra to Find Lengths
transversal | diagonal | parallelogram | algebra
DOK:
D
PTS: 1
DIF: L2
REF:
6-2.2 Use relationships among diagonals of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 3 Using Algebra to Find Lengths
KEY:
DOK 1
A
PTS: 1
DIF: L2
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 3 Using Algebra to Find Lengths
KEY:
DOK 2
3
6-2 Properties of Parallelograms
6-2 Properties of Parallelograms
parallelogram | angles
6-2 Properties of Parallelograms
parallelogram | angles
6-2 Properties of Parallelograms
parallelogram | consecutive angles
6-2 Properties of Parallelograms
6-2 Properties of Parallelograms
parallelogram | opposite angles
6-2 Properties of Parallelograms
DOK 2
6-2 Properties of Parallelograms
parallelogram | diagonal
6-2 Properties of Parallelograms
parallelogram | algebra
ID: A
26. ANS:
OBJ:
STA:
TOP:
DOK:
27. ANS:
OBJ:
STA:
TOP:
DOK:
A
PTS: 1
DIF: L3
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 4 Using Parallel Lines and Transversals
KEY:
DOK 2
C
PTS: 1
DIF: L2
REF:
6-2.1 Use relationships among sides and angles of parallelograms
MA.912.G.3.1| MA.912.G.3.2| MA.912.G.3.4| MA.912.G.4.5
6-2 Problem 4 Using Parallel Lines and Transversals
KEY:
DOK 1
4
6-2 Properties of Parallelograms
transversal | parallel lines
6-2 Properties of Parallelograms
parallel lines | transversal