Name: ________________________ Class: ___________________ Date: __________
Geometry A Final Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Name the line and plane shown in the diagram.
a.
b.
____



RS and plane RSU
c.
line R and plane RSU
d.



RS and plane U R



SR and plane U T



2. Which diagram shows plane PQR and plane QRS intersecting only in QR ?
a.
c.
b.
d.
1
ID: A
Name: ________________________
ID: A
____
3. Name the three labeled segments that are parallel to EF .
____
a. AB, CD, GH
4. Find AC.
____
a. 14
b. 15
c. 12
d. 4
5. If EF  2x  12, FG  3x  15, and EG  23, find the values of x, EF, and FG. The drawing is not to scale.
a.
b.
b.
GH , EG , CD
x = 10, EF = 8, FG = 15
x = 3, EF = –6, FG = –6
c.
c.
d.
BF , AB, CD,
d.
AC , CD, GH
x = 10, EF = 32, FG = 45
x = 3, EF = 8, FG = 15
____
6. If T is the midpoint of SU , find the values of x and ST. The diagram is not to scale.
____
a. x = 5, ST = 45
c. x = 10, ST = 60
b. x = 5, ST = 60
d. x = 10, ST = 45
7. If mEOF  26 and mFOG  38, then what is the measure of EOG? The diagram is not to scale.
____
a. 64
b. 12
c. 52
d. 76
8. DFG and JKL are complementary angles. mDFG = x  5 , and mJKL = x  9 . Find the measure of
each angle.
a. DFG = 47, JKL = 53
c. DFG = 52, JKL = 48
b. DFG = 47, JKL = 43
d. DFG = 52, JKL = 38
2
Name: ________________________
____
ID: A
9. Line r is parallel to line t. Find m5. The diagram is not to scale.
a.
45
b.
35
c.
135
____ 10. If BCDE is congruent to OPQR, then DE is congruent to
a.
PQ
b.
OR
c.
?
d.
145
d.
QR
.
OP
____ 11. What other information do you need in order to prove the triangles congruent using the SAS Congruence
Postulate?
a. BAC  DAC
c. AC  BD
b. CBA  CDA
d. AC  BD
____ 12. State whether ABC and AED are congruent. Justify your answer.
a.
b.
c.
d.
yes, by either SSS or SAS
yes, by SSS only
yes, by SAS only
No; there is not enough information to conclude that the triangles are congruent.
3
Name: ________________________
ID: A
____ 13. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?
a.
c.
b.
d.
____ 14. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
a. either ASA or AAS
c. AAS only
b. ASA only
d. neither
____ 15. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
a.
75 ft
b.
150 ft
c.
4
35.5 ft
d.
37.5 ft
Name: ________________________
ID: A
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem
you used.
____ 16.
a. ADB  CDB; SAS
c. ADB  CDB; SSS
b. ABD  CDB; SAS
d. The triangles are not similar.
____ 17. Which graph shows a triangle and its reflection image in the x-axis?
a.
c.
b.
d.
____ 18. Use an ordered pair to describe the translation that is 7 units to the left and 1 units down.
a.
7,  1
b.
7, 1
c.
5
7,  1
d.
7, 1
Name: ________________________
ID: A
____ 19. Which translation from solid-lined figure to dashed-lined figure is given by the vector 3, 3 ?
a.
c.
b.
d.
____ 20. Tell whether the three-dimensional object has rotational symmetry about a line and/or reflectional symmetry
in a plane.
a.
b.
c.
d.
reflectional symmetry
reflectional symmetry and rotational symmetry
rotational symmetry
no symmetry
6
Name: ________________________
ID: A


____ 21. Name the ray that is opposite BA .










a. BD
b. BA
c. CA
d. DA
____ 22. If mDEF  122, then what are mFEG and mHEG? The diagram is not to scale.
a. mFEG  122, mHEG  58
c. mFEG  68, mHEG  122
b. mFEG  58, mHEG  132
d. mFEG  58, mHEG  122
____ 23. Write this statement as a conditional in if-then form:
All triangles have three sides.
a. If a triangle has three sides, then all triangles have three sides.
b. If a figure has three sides, then it is not a triangle.
c. If a figure is a triangle, then all triangles have three sides.
d. If a figure is a triangle, then it has three sides.
____ 24. Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the
____ and the part following then is the ____.
a. conditional; conclusion; hypothesis
c. conditional; hypothesis; conclusion
b. hypothesis; conclusion; conditional
d. hypothesis; conditional; conclusion
____ 25. Write the two conditional statements that make up the following biconditional.
I drink juice if and only if it is breakfast time.
a. I drink juice if and only if it is breakfast time.
It is breakfast time if and only if I drink juice.
b. If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.
c. If I drink juice, then it is breakfast time.
I drink juice only if it is breakfast time.
d. I drink juice.
It is breakfast time.
7
Name: ________________________
ID: A
Fill in each missing reason.
____ 26. Given: 11x  6y  1; x  8
Prove:
89
y
6
11x  6y  1; x  8
a. ________
88  6y  1
b. ________
6y  89
c. ________
89
6
d. ________
y
89
y
e. ________
6
a. a. Given
b. Symmetric Property of Equality
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
b. a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Symmetric Property of Equality
c.
d.
a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Division Property of Equality
e. Reflexive Property of Equality
a. Given
b. Substitution Property
c. Subtraction Property of Equality
d. Addition Property of Equality
e. Symmetric Property of Equality
Use the given property to complete the statement.
____ 27. Substitution Property of Equality
If y  3 and 8x  y  12 , then ______.
a. 8(3)  y  12
b. 3  y  12
c.
d.
8x  3  12
8x  3  12
c.
19
____ 28. Find the value of x.
a.
–19
b.
125
8
d.
55
Name: ________________________
ID: A
____ 29. m3  37. Find m1.
a. 37
b. 143
____ 30. Which angles are corresponding angles?
a.
b.
8 and 16
7 and 8
c.
27
c.
d.
4 and 8
none of these
9
d.
153
Name: ________________________
ID: A
____ 31. Which is a correct two-column proof?
Given: l  m
Prove: p and k are supplementary.
a.
Statements
R e asons
1. l  m
1. Given
2. p  d
2. Vertical Angles
3. d and c are supplementary.
3. Same-Side Interior Angles
4. c  k
4. Vertical Angles
5. p and k are supplementary.
5. Substitution
Statements
R e asons
1. l  m
1. Given
2. p  k
2. Corresponding Angles
3. d and c are supplementary.
3. Same-Side Exterior Angles
4. c  k
4. Vertical Angles
5. d and k are supplementary.
5. Substitution
Statements
R e asons
1. l  m
1. Given
2. p  d
2. Vertical Angles
3. b and k are supplementary.
3. Alternate Interior Angles
4. c  k
4. Vertical Angles
5. p and k are supplementary.
5. Same-Side Interior Angles
b.
c.
d.
none of these
10
Name: ________________________
ID: A
____ 32. Name the theorem or postulate that lets you immediately conclude ABD  CBD.
a.
SAS
b.
ASA
c.
AAS
d.
none of these
d.
0, 15
Use the diagram.
____ 33. Find the vector that describes the translation B  A.
a.
8, 14
b.
7, 2
c.
4, 10
____ 34. Write a rule to describe the transformation that is a reflection in the y-axis.
a. (x, y)  (x, –y)
c. (x, y)  (–x, –y)
b. (x, y)  (–x, y)
d. (x, y)  (y, x)
____ 35. Find mQ. The diagram is not to scale.
a.
76
b.
104
c.
11
66
d.
114
Name: ________________________
____ 36. What is the graph of 4x  7y  28?
a.
b.
ID: A
c.
d.
12
Name: ________________________
ID: A
____ 37. What is the graph of y  (1)  1 / 2(x  (2)) ?
a.
c.
b.
d.
____ 38. What is an equation in slope-intercept form for the line given?
a.
b.
y  1 / 2x  (1 / 2)
y  1 / 2x  (5)
c.
d.
13
y  2x  (1 / 2)
y  2x  (9 / 2)
Name: ________________________
ID: A
____ 39. What is the equation in point-slope form for the line parallel to y = 3x + 2 that contains P(–7, –6)?
a. y – 6 = 3(x + 7)
c. y + 6 = –3(x + 7)
b. x + 6 = –3(y + 7)
d. y + 6 = 3(x + 7)
____ 40. What is an equation in point-slope form for the line perpendicular to y = 3x + 9 that contains (–6, 5)?
1
a. x – 5 = 3(y + 6)
c. y – 6 =  (x + 5)
3
1
b. y – 5 =  (x + 6)
d. y – 5 = 3(x + 6)
3
____ 41. Are the lines y = –x – 2 and 4x + 4y = 16 perpendicular? Explain.
a. Yes; their slopes have product –1.
b. No; their slopes are not opposite reciprocals.
c. Yes; their slopes are equal.
d. No; their slopes are not equal
____ 42. Which pair of triangles is congruent by ASA?
a.
c.
b.
d.
14
Name: ________________________
ID: A
____ 43. Supply the missing reasons to complete the proof.
Given: Q  T and QR  TR
Prove: PR  SR
Statement
1. Q  T and
Reasons
1. Given
QR  TR
2. PRQ  SRT
2. Vertical angles are congruent.
3. PRQ  SRT
3.
?
4. PR  SR
4.
?
a. ASA; Substitution
c. AAS; Corresp. parts of   are .
b. SAS; Corresp. parts of   are .
d. ASA; Corresp. parts of   are .
____ 44. For which situation could you immediately prove 1  2 using the HL Theorem?
a.
I only
b.
II only
c.
15
III only
d.
II and III
Name: ________________________
ID: A
____ 45. Find the value of x.
a.
4
b.
8
c.
6.6
d.
6
Short Answer
46. Is PQS  RQS by HL? If so, name the legs that allow the use of HL.
47. Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and
name the postulate you would use. If no, write not possible and tell what other information you would need.
48. a. Graph the quadrilateral WXYZ with vertices W(3, –5), X(1, –3), Y(–1, –5), and Z(1, –7).
b. Rotate the figure 90° counterclockwise around the origin and graph the rotation.
16
Name: ________________________
ID: A
49. The dashed triangle is a dilation image of the solid triangle. Find the center and scale factor of the dilation.
Use scalar multiplication to find the image vertices for a dilation with center (0, 0) and the given scale
factor.
50. scale factor 4
17
Name: ________________________
ID: A
Fill in each missing reason.
51. Given: mAOC  150
mAOB  mBOC  mAOC
a. ____
2x  6(x  3)  150
b. ____
2x  6x  18  150
c. ____
8x  18  150
d. ____
8x  168
e. ____
x  21
f. ____
52. Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given: l  n
Prove: 4  6
Statements
Reasons
1.
l  n
1.
Given
2.
2  6
a.
?
3.
4  2
b.
?
4.
6  4
c.
?
18
Name: ________________________
ID: A
53. State the missing reasons in this proof.
Given: 1  5
Prove: p  r
Statements
Reasons
1. 1  5
Given
2. 4  1
a.____
3. 4  5
b.____
4. p  r
c.____
54. Write the missing reasons to complete the proof.
Given: AB  CD, A  D, and AF  DE
Prove: FAC  EDB
Statement
1. AF  DE
2. A  D
3. AB  CD
4. AB  CD
5. AB  BC  CD  BC
6. AC  BD
7. AC  BD
8. FAC  EDB
Reason
1. Given
2. Given
3. Given
4. Definition of congruent segments
5. ?
6. Segment Addition Postulate
7. Definition of congruent segments
8. ?
19
Name: ________________________
ID: A
55. Complete the proof by providing the missing reasons.
Given: SD  HT; SH  ST
Prove: SHD  STD
Statement
1. SD  HT
2. SDH and SDT are right s
3. SH  ST
4. ?
5. SHD  STD
Reason
1. Given
2. ?
3. ?
4. Reflexive Property
5. ?
20
Name: ________________________
ID: A
56. Write the missing reasons to complete the flow proof.
Given: ADB and CDB are right angles, A  C
Prove: ADB  CDB
21
Name: ________________________
ID: A
57. Complete the proof by providing the missing reasons.
Given: CB  BD , DE  EC, CB  DE
Prove: DBC  CED
Statement
Reason
1. CB  DE , CB  BD , and DE  EC
1. Given
2. CBD and DEC are right angles
3. CBD  DEC
4. CD  CD
5. DBC  CED
2. Definition of perpendicular segments
3. ?
4. ?
5. ?
Essay
58. Write a two-column proof.
Given: BC  EC and AC  DC
Prove: BA  ED
22
Name: ________________________
ID: A
59. Write a proof.
Given: BC  DA , 1  2, and CF  AF
Prove: CFE  AFE
Other
60. Given that EAC  ECA, what else do you need to prove that BA  DC ? Outline a proof that uses the
needed information.
23