Download Geometry Benchmark Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry Benchmark Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Use the figure below.
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1. For the cube shown, AD and HG are ___________.
a. parallel lines b. oblique lines c. skew lines d. perpendicular lines
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2. In the figure, 1 and 2 are _________.
a. alternate exterior angles b. alternate interior angles c. consecutive interior angles d. corresponding angles
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Name: ________________________
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ID: A
3. In the figure, 6 and 3 are __________.
a. alternate exterior angles b. consecutive interior angles c. corresponding angles d. alternate interior angles
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4. In the figure, 6 and 2 are _____________.
a. alternate interior angles b. consecutive interior angles c. alternate exterior angles d. corresponding angles
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5. Find m1 in the figure below. PQ and RS are parallel.
a. 17° b. 73° c. 97° d. 107°
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Name: ________________________
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ID: A
6. In the figure, l  n and r is a transversal. Which of the following is not necessarily true?
a. 8  2 b. 2  6 c. 5  3 d. 7  4
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7. In the figure shown, HC  GD and mABC = 105°. Which of the following statements is false?
a. mDEF  75° b. ABH and AEG are corresponding angles. c. HBF and AED are alternate
interior angles. d. mGEF  75°
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8. Use the figure to find the measure of 6
a. 125° b. 80° c. 55° d. 145°
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Name: ________________________
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ID: A
9. If AC is parallel to DF , what is the measure, in degrees, of ABD?
a. 28° b. 72° c. 62° d. 38°
____ 10. Line m is parallel to line n and they are each intersected by the same two transversals. Which angle is NOT
necessarily congruent to 4
a. 12 b. 16 c. 7 d. 15
____ 11. A photographer shines a camera light at a particular painting forming an angle of 47° with the camera
platform. If the light is 52 feet from the wall where the painting hangs, how high above the platform is the
painting?
a. 0.93 ft b. 55.76 ft c. 1.07 ft d. 48.49 ft
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Name: ________________________
ID: A
____ 12. Use the graph below to complete the sentence.
Figure AB C D  is the image of figure ABCD under a rotation _______
a. 180° about the origin. b. 90° counterclockwise about the origin. c. 270° counterclockwise about the
origin. d. 270° clockwise about the origin.
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Name: ________________________
ID: A
____ 13. The transformation  x, y    x,  y  is applied to the figure below. Identify the image of the figure under
this transformation.
a.
c.
b.
d.
____ 14. A rectangular field is 280 m by 390 m. A rectangular barn 25 m by 33 m is built in the field. How much area is
left over?
2
2
2
2
a. 110 025 m b. 108 375 m c. 109 142 m d. 108 388 m
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Name: ________________________
ID: A
____ 15. A rectangular garden, 42 feet by 20 feet, is surrounded by a walkway of uniform width. If the total area of the
garden and walkway is 1248 square feet, the width of the walkway is _______.
a. 2 ft b. 3 ft c. 2.5 ft d. 3.29 ft
____ 16. A rectangle has length l and width w. An expression for its area is _____.
a. 2(l + w) b. l2  w2
c. l  w d. lw
Short Answer
17. Sketch an example of consecutive interior angles.
True or False:
18. If two parallel lines are intersected by a transversal, then consecutive interior angles are complementary.
19. Use the figure to find the measure of 1
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Name: ________________________
ID: A
20. A dirt path connects the lanes of a divided highway that runs east-west. An officer in a police car headed east
gets a call that requires crossing over to the westbound lanes using the dirt path.
Through what angle must the police car turn at the bend in the dirt path?
21. What is the length of the diagonal of a square with side lengths 7 2?
22. The length of the diagonal of a square is 22. What is the length of each side?
23. A baseball "diamond" is a square with a side length of 90 feet. How far is the throw from third base to first
base? (Round your answer to one decimal place.)
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Name: ________________________
ID: A
24. A tree 18 feet tall casts a shadow which forms an angle of 50° with the ground. How long is the shadow to the
nearest hundredth?
Writing:
25. Explain how a tangent ratio can be used to find the height of the building in the figure below. Find the height of
the building when A = 42°.
26. Graph the triangle whose vertices have the coordinates given below. Then draw its reflection in the x-axis.
(–6, 3), (–3, 3), (–5, 8)
27. The figure below is made up of two squares with the areas shown. What is the length of x?
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Name: ________________________
ID: A
28. A farmer has a four-sided farm with opposite sides parallel. One pair of sides runs east and west. They are
160 meters apart, and are both 330 meters wide. How large, in square meters, is the farm?
Essay
29. Open-ended Problem: Two lines can be parallel, two planes can be parallel, and a line and a plane can be
parallel. Do you think two circles can be parallel? Explain why or why not. (Hint: Consider slicing through a
globe at two of its lines of latitude.
Other
Complete this two-column proof.
30. Given: Lines m and n are parallel.
Transversal t intersects lines m and n.
Prove: m1  m7
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Statements
Reasons
1. m  n t intersects m and n
1. Given
2. m1=m3; m5=m7
2.____________________
3. m3=m5
3.____________________
4. m1=m5
4.____________________
5. m1=m7
5.____________________
31. Given: Lines q and r are parallel.
Transversal t intersects lines q and r.
Prove: 2 and 7 are supplementary.
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Name: ________________________
ID: A
32. Given: Lines q and r are parallel.
Transversal t intersects lines q and r.
Prove: m2=m8
33. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.
Lines a and b in the figure below are parallel.
What is the measure of  1 in degrees?
True or False:
34. The area of a triangle is found by multiplying the length of its base by its height.
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Name: ________________________
ID: A
35. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet.
What is the area of the figure below, in square inches?
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ID: A
Geometry Benchmark Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
C
A
B
D
D
D
D
A
A
B
B
C
A
B
B
C
SHORT ANSWER
17.
18.
19.
20.
21.
Sketches vary.
False
52°
96°
14
22. 11 2
23. 127.3 ft
24. 15.1 ft
25. Using the tangent ratio tan A 
leg opposite A
h


 tan 42 o 
 So h  120  tan 42 o   120 0.9 or
leg adjacent to A
120


about 108 ft.
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ID: A
26.
27. 150
28. 52,800 m2
ESSAY
29. Both answers could be supported here. Some circles do not intersect just like some lines do not. But circles are
bounded and maybe should not be compared to lines. Research on non-Euclidean geometry will give students
more information about this concept.
OTHER
30.
Statements
Reasons
1. NA
1. NA
2. NA
2. Vertical angles are=in measure.
3. NA
3. If 2 || lines are intersected by a transversal,
then alternate interior angles are = in measure.
4. NA
4. Substitution property (Steps 2 and 3)
5. NA
5. Substitution property (Steps 2 and 4)
Statements
Reasons
1. q  r transversal t
1. Given
2. m2=m4, m7=m5
2. Vertical angles are = in measure.
31. 3. 4 and 5 are supplementary.
3. If two || lines are intersected by a transversal,
then consecutive interior angles are supplementary.
4. m4+m5=180 o
4. Defintion of supplementary angles
5. m2+m7=180 o
5. Substitution property (Steps 2 and 4)
6. 2 and 7 are supplementary.
6. Definition of supplementary angles
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ID: A
Statements
Reasons
1. q  r transversal t
1. Given
32. 2. m2=m6
2. If 2 || lines are intersected by a transversal,
then corresponding angles are = in measure.
3. m6=m8
3. Vertical angles are = in measure.
4. m2  m8
4. Substitution property (Steps 2 and 3)
33. 77
34. False
35. 317.5
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