Download Geometry 1-1 to 1-4 Practice Problems

Name: ______________________
Class: _________________
Date: _________
Geometry 1-1 to 1-4 Practice Problems
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. How many planes can be drawn through any three non collinear points?
a.
0
b.
1
c.
2
d.
3
d.
F, E, G
Use the figure below to answer the following questions.
____
2. Which three points in the figure are collinear?
a.
____
b.
A, B, C
c.
E, C, A
3. Name the intersection of the plane P and the plane that contains points B, C, and D.
a.
____
A, B, D
point B
b.
←⎯
⎯
→
BC
c.
BD
d.
ΔBCD
d.
3
d.
A, D, E
4. Suppose A and B are points. How many lines contain both A and B?
a.
0
b.
1
c.
2
Use the figure below to answer the following questions.
____
5. Which three points in the figure are collinear?
a.
C, D, F
b.
A, E, F
c.
1
B, C, D
ID: A
Name: ______________________
____
6. Name the intersection of the plane that contains points A, B, and D and the plane P.
a.
____
ID: A
point D
b.
triangle BCD
c.
AD
4
b.
40
c.
56
c.
n
d.
p
c.
d.
H
JDB
Refer to Figure 1.
Figure 1
8. Name a line that contains point J.
a.
b.
____
←⎯
⎯
→
BD
7. Given A is between Y and Z and YA = 14x, AZ = 10x and YZ = 12x + 48, find AZ.
a.
____
d.
←⎯
⎯
→
DB
←⎯
⎯
→
GF
9. Name the plane containing lines m and p.
a. n
b. GFC
____ 10. What is another name for line n?
a.
b.
line JB
←⎯
⎯
→
DC
____ 11. What is another name for line m?
a. line JG
b.
←⎯⎯
⎯
→
JGB
c.
←⎯
⎯
→
GF
d.
AC
c.
DB
d.
line JB
c.
d.
K
____ 12. Name a line that contains point A.
a.
b.
←⎯
⎯
→
DC
m
2
DB
d.
96
Name: ______________________
ID: A
←⎯
⎯
→
←⎯
⎯
→
____ 13. Name a point NOT contained in AD or FG .
a. K
c.
b. A
d.
____ 14. Which is these is NOT a way to refer to line BD?
a.
b.
←⎯
→
JB
m
c.
d.
H
D
←⎯⎯
⎯
→
JDB
line JD
____ 15. Name three points that are collinear.
a.
b.
B, G, F
C, D, H
c.
d.
J, G, F
J, D, G
c.
d.
Q, L, M
R, S, K
____ 16. Name three points that are collinear.
a.
b.
M, L, R
L, P, T
3
Name: ______________________
ID: A
____ 17. Lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b. Draw and label a
figure for the relationship.
a.
c.
b.
d.
Refer to Figure 2.
Figure 2
____ 18. Name three collinear points.
a. B, L, D
b. C, L, B
c.
d.
K, A, C
D, F, G
____ 19. Name a point that is NOT coplanar with G, A, and B.
a. K
c. C
b. D
d. F
4
Name: ______________________
ID: A
____ 20. Name four points that are coplanar.
a. G, D, L, B
b. C, K, A, G
c.
d.
L, A, C, G
K, B, D, L
____ 21. Name an intersection of plane GFL and the plane that contains points A and C.
a. line LC
c. line AC
b. C
d. plane CAB
____ 22. Which plane(s) contain point K?
a. plane AGC
b. plane ADB, plane ALC
c.
d.
plane CAG, plane ABD
plane DBA
____ 23. Which three-dimensional figure matches this net?
a.
c.
b.
d.
____ 24. ____ two points are collinear.
a. Any
b.
Sometimes
5
c.
No
Name: ______________________
ID: A
←⎯
⎯
→
____ 25. Which diagram shows plane PQR and plane QRS intersecting only in QR ?
a.
c.
b.
d.
____ 26. “ Two points determine a line.”
Which of the following best describes the statement above?
a.
b.
theorem
postulate
c.
d.
formula
undefined term
____ 27. Which of the following best defines an axiom?
a.
b.
c.
d.
finding a pattern in specific cases and then writing a statement for the general case
an unproven statement that is based on observations
a rule that is accepted without proof
a proven statement used in a proof
Short Answer
28. If EF = 6 and EG = 21, find the value of FG. The drawing is not to scale.
29. If EF = 5x + 15, FG = 53, and EG = 143, find the value of x. The drawing is not to scale.
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Name: ______________________
ID: A
30. If EF = 2x − 12, FG = 3x − 15, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale.
31. If Z is the midpoint of RT, what are x, RZ, and RT?
32. Which point is the midpoint of AE?
33. If T is the midpoint of SU, what are ST, TU, and SU?
34. If m∠AOC = 85°, m∠BOC = 2x + 10, and m∠AOB = 4x − 15, find the degree measure of
∠BOC and ∠AOB. The diagram is not to scale.
35. If m∠EOF = 26 and m∠FOG = 38, then what is the measure of ∠EOG? The diagram is not to scale.
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Name: ______________________
ID: A
Refer to Figure 1.
Figure 1
36. Name a point NOT contained in lines m, n, or p.
37. Name the intersection of lines m and n.
38. Does line p intersect line m or line n? Explain.
Refer to Figure 2.
Figure 2
39. How many planes are shown in the figure?
40. How many planes contain points B, C, and A?
41. Where could you add point M on plane LBD so that D, B, and M would be collinear?
42. How many planes contain points B, L, F, and D?
43. Name the intersection of plane KCG and a plane that contains points L and D.
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Name: ______________________
ID: A
Find the measurement of the segment.
44. PR = 18.8 mm, RS = 13.7 mm
PS = ?
45. QT = 0.4 in., QV = 1.9 in.
TV = ?
46. Find the value of the variable and GH if H is between G and I.
GI = 5b + 1, HI = 4b − 5, HI = 7
Use the number line to find the measure.
47. PH
48. RK
Measure the angle.
49.
9
Name: ______________________
ID: A
50.
Measure the angle and classify it as right, acute, or obtuse.
51. ∠1
52. ∠FGB
53. What is a net for the figure below?
10
Name: ______________________
ID: A
54. Are O, N, and P collinear? If so, name the line on which they lie.
55. Name the plane represented by the front of the box.
56. Are points B, J, and C collinear or noncollinear?
57. Name the ray in the figure.
⎯⎯
→
58. Name the ray that is opposite BA .
59. Find AC.
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Name: ______________________
ID: A
60. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale.
61. If m∠EOF = 26 and m∠FOG = 38, then what is the measure of ∠EOG? The diagram is not to scale.
62. If m∠BOC = 27 and m∠AOC = 47, then what is the measure of ∠AOB? The diagram is not to scale.
Use the figure below to answer the following questions.
63. Name three points on plane P.
64. Name the intersection of planes P and N.
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Name: ______________________
ID: A
Use the figure below to answer the following questions.
65. What is another name for line m?
66. Name three points on plane B.
67. Name the intersection of planes A and B.
68. Name three non collinear points.
69. Find the length of DE.
70. Measure ∠ABC. Then classify ∠ABC as right, acute, or obtuse.
Use the figure below to answer the following questions.
←⎯
⎯
→
←⎯
⎯
→
71. Name a line that is coplanar with AD and AB .
72. Find the value of y if AC = 3y + 5, CB = 4y – 1, AB = 9y – 12, and point C lies between A and B.
13
Name: ______________________
ID: A
73. Name four rays shown.
74. Describe a real-life example of two planes and their intersection.
75. On a number line, P has coordinate –47 and Q has coordinate 40. Find PQ.
76. Are BC and DE congruent? Explain.
77. What are three names for the angle?
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