Download geometry - Swampscott High School

GEOMETRY
(edited by Monteiro)
1. Grade 10 | Mathematics | Multiple Choice | 2005 | Question 38
Reporting Category: Geometry Standard(s): 10.G.5
Each of the two interior supports for part of a roof is perpendicular to a rafter, as shown below.
What is x, the measure, in degrees, of the angle formed by the two interior supports?
A. 50
B. 65
C. 90
D. 130
GEOMETRY
2. Grade 10 | Mathematics | Multiple Choice | 2005 | Question 32
Reporting Category: Geometry Standard(s): 10.G.5
A kite has perpendicular diagonals with the measures shown in the drawing below.
What is the perimeter, in inches, of the kite?
A. 130
B. 165
C. 260
D. 310
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GEOMETRY
(edited by Monteiro)
3. Grade 10 | Mathematics | Multiple Choice | 2005 | Question 29
Reporting Category: Geometry Standard(s): 10.G.6
The diagram below shows the side view of a house. The base of its roof is 4 meters above ground level.
Point P is the highest point on the roof. Based on the diagram, what is the distance from P to ground level?
A. 6 m
B. 7 m
C. 10 m
D. 13 m
GEOMETRY
(edited by Monteiro)
4. Grade 10 | Mathematics | Multiple Choice | 2005 | Question 25
Reporting Category: Geometry Standard(s): 10.G.7
has one endpoint at A(2, 5), and its midpoint is at (4, 0). What are the coordinates of B, the other
endpoint of
?
A. (2, −5)
B. (3, 2.5)
C. (6, −5)
D. (6, 2.5)
GEOMETRY
(edited by Monteiro)
5. Grade 10 | Mathematics | Multiple Choice | 2004 | Question 36
Reporting Category: Geometry Standard(s): 10.G.5
What is the measure of
A. 34°
B. 56°
C. 62°
D. 68°
B in the figure below?
GEOMETRY
(edited by Monteiro)
6. Grade 10 | Mathematics | Multiple Choice | 2004 | Question 33
Reporting Category: Geometry Standard(s): 10.G.5
Using the measures shown in the sketch, what is the length of the section of the ladder from the point where
it rests on the ground to the point where it touches the house
?
A. 4.8 ft.
B. 7 ft.
C. 17 ft.
D. 23 ft.
GEOMETRY
(edited by Monteiro)
7. Grade 10 | Mathematics | Multiple Choice | 2004 | Question 26
Reporting Category: Geometry Standard(s): 10.G.8
Which of the following is an equation for a line that is not parallel to the line with this equation?
−x + 4y − 8 = 0
A. y = ¼x − 1
B. y = ¼x + 21
C. −2x + 4y − 8 = 0
D. −x + 4y + 8 = 0
GEOMETRY
8.
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Grade 10 | Mathematics | Multiple Choice | 2004 | Question 25
Reporting Category: Geometry Standard(s): 10.G.4
In the figures shown below, ΔABC is similar to
ΔXYZ.
What is the length of
A. 2.0 cm
B. 4.5 cm
C. 12.5 cm
D. 22.5 cm
?
GEOMETRY
9. Grade 10 | Mathematics | Multiple Choice | 2004 | Question 10
Reporting Category: Geometry Standard(s): 10.G.1
A partial drawing of a quadrilateral is shown below.
If no other sides or angles are congruent, which best describes the figure?
A. square
B. rectangle
C. parallelogram
D. trapezoid
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GEOMETRY
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10. Grade 10 | Mathematics | Multiple Choice | 2003 | Question 40
Reporting Category: Geometry Standard(s): 10.G.4
A cup in the shape of a cone has a height of 8 units and a radius of 4 units as shown in the figure below. The
water in the cup reaches a height of 5 units.
What is the value of r, the radius of the surface of the water?
A. 1.6 units
B. 2.5 units
C. 6.4 units
D. 10.0 units
GEOMETRY
(edited by Monteiro)
11. Grade 10 | Mathematics | Multiple Choice | 2003 | Question 33
Reporting Category: Geometry Standard(s): 10.G.9
The diagram below shows the location of
Suppose that
E?
is rotated 180° clockwise about the origin. What are the coordinates of the image of point
A. (−2, −4)
B. (−4, −2)
C. (4, −2)
D. (−4, 2)
on a coordinate plane.
GEOMETRY
12. Grade 10 | Mathematics | Multiple Choice | 2003 | Question 25
Reporting Category: Geometry Standard(s): 10.G.9
The diagram below shows ΔPQR on a coordinate plane.
Which of the following is the result of a reflection of ΔPQR?
A.
B.
C.
D.
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GEOMETRY
13.
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Grade 10 | Mathematics | Multiple Choice | 2003 | Question 9
Reporting Category: Geometry Standard(s): 10.G.4
In the figure shown below, triangle TUV is formed by joining the midpoints of the sides of equilateral triangle
QRS. Triangle WYZ is formed by joining the midpoints of the sides of triangle TUV.
If the area of triangle QRS is 64 square inches, what is the area of triangle WYZ?
A. 1 square inch
B. 4 square inches
C. 8 square inches
D. 16 square inches
GEOMETRY
14. Grade 10 | Mathematics | Multiple Choice | 2003 | Question 7
Reporting Category: Geometry Standard(s): 10.G.7
You may use the grid below to answer question
On the coordinate plane, what is the distance between the points (3, 4) and (11, 10)?
A. 10
B. 7
C. 5
D. 14
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GEOMETRY
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15. Grade 10 | Mathematics | Multiple Choice | 2006 | Question 9
Reporting Category: Geometry Standard(s): 10.G.1
Which of the following must be true for the rhombus shown below?
A. m
DAB = m
ABC
B. m
DAB + m
ABC = 90°
C. m
DAC + m
BAC = 90°
D. m
DAC = m
BAC
GEOMETRY
16. Grade 10 | Mathematics | Multiple Choice | 2006 | Question 39
Reporting Category: Geometry Standard(s): 10.G.1
A polygon was drawn on a piece of paper.
•
•
Each of its interior angles has the same measure.
The sum of the measures of its interior angles is 360°.
Which of the following could be the polygon?
A. a rectangle
B. a regular hexagon
C. a regular pentagon
D. an equilateral triangle
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GEOMETRY
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17. Grade 10 | Mathematics | Multiple Choice | 2006 | Question 36
Reporting Category: Geometry Standard(s): 10.G.9
The coordinates of four points are given below.
A (3, 3)
A' (−3, 3)
B (4, −4)
B ' (4, 4)
Which of the following transformations maps
to
?
A. reflection across the x-axis
B. reflection across the y-axis
C. 90° counterclockwise rotation about the origin
D. 180° counterclockwise rotation about the origin
GEOMETRY
(edited by Monteiro)
18. Grade 10 | Mathematics | Multiple Choice | 2006 | Question 28
Reporting Category: Geometry Standard(s): 10.G.6
A square has a side of length 12 centimeters. Which of the following is closest to the length of a diagonal of
the square?
A. 12 cm
B. 17 cm
C. 21 cm
D. 24 cm
GEOMETRY
(edited by Monteiro)
19. Grade 10 | Mathematics | Multiple Choice | 2008 | Question 39
Reporting Category: Geometry Standard(s): 10.G.11
The vertex-edge graph below represents all the paths in a park.
Mike is at point J and wants to walk along each path exactly one time. At which point will Mike finish his
walk?
A. point K
B. point M
C. point N
D. point P
GEOMETRY
(edited by Monteiro)
20. Grade 10 | Mathematics | Multiple Choice | 2008 | Question 37
Reporting Category: Geometry Standard(s): 10.G.6
If the length of
is 20 centimeters. What is the length of
A. 10 cm
B. 10
cm
C. 20 cm
D. 20
cm
?
GEOMETRY
21. Grade 10 | Mathematics | Multiple Choice | 2008 | Question 36
Reporting Category: Geometry Standard(s): 10.G.3
What is
A. 30°
B. 50°
C. 60°
D. 70°
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GEOMETRY
22. Grade 10 | Mathematics | Multiple Choice | 2008 | Question 26
Reporting Category: Geometry Standard(s): 10.G.10
The rectangle below is a cross section of a three-dimensional object.
The rectangle could not be a cross section of which of the following objects?
A. a cylinder
B. a prism
C. a cube
D. a cone
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GEOMETRY
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23. Grade 10 | Mathematics | Multiple Choice | 2007 | Question 36
Reporting Category: Geometry Standard(s): 10.G.3
The lines in the diagram below represent four streets in Linda's hometown.
Keller Street is parallel to Garcia Street, and Main Street is parallel to Second Street.
If m
1 = 95°, what is m
A.
75°
B.
85°
C.
95°
D.
105°
2?
GEOMETRY
(edited by Monteiro)
24. Grade 10 | Mathematics | Multiple Choice | 2007 | Question 29
Reporting Category: Geometry Standard(s): 10.G.5
Triangle XYZ and two angle measures are shown in the diagram below.
What is the measure of
A.
50°
B.
85°
C.
90°
D.
95°
Y?
GEOMETRY
25. Grade 10 | Mathematics | Multiple Choice | 2007 | Question 27
Reporting Category: Geometry Standard(s): 10.G.6
An equilateral triangle and its side lengths are shown below.
What is h, the height of the equilateral triangle?
A.
3 cm
B.
4 cm
C.
3
cm
D.
3
cm
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GEOMETRY
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26. Grade 10 | Mathematics | Multiple Choice | 2007 | Question 12
Reporting Category: Geometry Standard(s): 10.G.11
The line segments in the diagram below represent the paths through a rose garden.
If Roberta starts at point P and walks on each path exactly once, at what point will she finish?
A.
Q
B.
R
C.
S
D.
T
GEOMETRY
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27. Grade 10 | Mathematics | Multiple Choice | 2009 | Question 40
Reporting Category: Geometry Standard(s): 10.G.5
Triangle PQR in the diagram below represents Pam’s trip across a river.
In the diagram, PQ represents her planned trip across the river, and PR represents her actual trip across the
river.
Based on the dimensions in the diagram, which of the following is closest to the length of PR ?
A. 104 feet
B. 117 feet
C. 120 feet
D. 160 feet
GEOMETRY
(edited by Monteiro)
28. Grade 10 | Mathematics | Multiple Choice | 2009 | Question 38
Reporting Category: Geometry Standard(s): 10.G.9
The coordinates of the endpoints of ST and its image S'T' are given below.
S (2, –4)
T (–1, 1)
S' (–2, –4)
T' (1, 1)
Which of the following single transformations maps ST to S'T' ?
A. translation 4 units to the left
B. rotation 180° clockwise about the origin
C. reflection over the x-axis
D. reflection over the y-axis
GEOMETRY
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29. Grade 10 | Mathematics | Multiple Choice | 2009 | Question 30
Reporting Category: Geometry Standard(s): 10.G.4
In the diagram below,
MNP ~
RST.
Based on the dimensions in the diagram, what is the length of MN?
A. 15 in.
B. 24 in.
C. 30 in.
D. 40 in.
GEOMETRY
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30. Grade 10 | Mathematics | Multiple Choice | 2009 | Question 23
Reporting Category: Geometry Standard(s): 10.G.3
In the diagram below, lines k, m, and n are parallel lines intersected by line p.
Line p is not perpendicular to lines k, m, and n.
Which of the following angles has a measure that is not equal to the measure of
A.
2
B.
3
C.
4
D.
5
1?
GEOMETRY
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31. Grade 10 | Mathematics | Multiple Choice | 2009 | Question 8
Reporting Category: Geometry Standard(s): 10.G.1
Exactly three diagonals can be drawn from each vertex of a given polygon. What is the total number of sides
of the polygon?
A. 3
B. 4
C. 5
D. 6
GEOMETRY
32.
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Grade 10 | Mathematics | Open Response | 2005 | Question 20
Reporting Category: Geometry Standard(s): 10.G.7, 10.M.1
A landscaper's scale model of a patio is shown on the coordinate plane below. All of the corners of the patio
form right angles, and the patio has both a horizontal and a vertical line of symmetry. The coordinates of
some of the vertices are shown.
Scale
1 unit represents 1 yard
a. What is the total perimeter of the patio, in yards? Show or explain how you got your answer.
b. What is the total area of the patio, in square yards? Show or explain how you got your answer.
c.
A circular fountain will be placed in the center of the patio at the point where the patio’s lines of
symmetry intersect. What are the coordinates of the point that shows where the center of the fountain
will be placed? Show or explain how you got your answer.
GEOMETRY
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33. Grade 10 | Mathematics | Open Response | 2004 | Question 21
Reporting Category: Geometry Standard(s): 10.G.7
The graph of square ABCD is shown below.
a. What is the slope of diagonal
of the square? Show or explain how you got your answer.
b. What is the slope of diagonal
of the square? Show or explain how you got your answer.
c.
What is the equation of the line containing diagonal
your answer.
of the square? Show or explain how you got
d. What is the equation of the line containing diagonal
your answer.
of the square? Show or explain how you got
e. What is the relationship between the line containing diagonal
of the square? Explain your answer.
and the line containing diagonal
GEOMETRY
34.
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Grade 10 | Mathematics | Open Response | 2003 | Question 41
Reporting Category: Geometry Standard(s): 10.G.7
When a map of the Caribbean Sea is placed on a grid, Island A is represented by A (2, 1), and Island B is
represented by B (6, 4). Graph and label these points on a coordinate grid
a. What is the length of line segment
on the grid? Show or explain how you got your answer.
b. If each unit on the grid represents 12 actual miles, what is the shortest distance in miles from Island
A to Island B? Show or explain how you got your answer.
c.
On the same map and grid, Island C is represented by C (2, 3). Graph point C on the same grid used
in part a. What is the least possible number of miles in a complete round trip of the three islands?
(From A to B to C and back to A). Show or explain your answer.
GEOMETRY
35.
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Grade 10 | Mathematics | Open Response | 2006 | Question 42
Reporting Category: Geometry Standard(s): 10.G.6
The diagram below shows a kitchen floor plan. When architects design a kitchen, they often consider the
distances between the following three major work locations shown in the diagram:
•
•
•
the refrigerator, indicated by R
the sink, indicated by S
the cooking area, indicated by C
When these three locations are connected, a triangle known as the "Work Triangle" is formed. This is the
area that has the highest amount of traffic in a kitchen. The shaded area in the diagram is the Work Triangle.
a) What is d, the distance, in feet, along the side of the Work Triangle from the sink to the refrigerator?
Show or explain how you got your answer.
b) What is h, the height, in feet, of the Work Triangle? Show or explain how you got your answer.
c) What is the area, in square feet, of the Work Triangle? Show or explain how you got your answer.
GEOMETRY
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36. Grade 10 | Mathematics | Open Response | 2008 | Question 17
Reporting Category: Geometry Standard(s): 10.G.8
Line j is represented by the equation below.
line j: y = 2x + 4
a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point with coordinates
(3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through the point with
coordinates (8, 10). Show or explain how you got your answer.
GEOMETRY
37.
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Grade 10 | Mathematics | Open Response | 2007 | Question 42
Reporting Category: Geometry Standard(s): 10.G.6
A diagram of part of a baseball field and some of its dimensions are shown below. Point F represents First
Base, point S represents Second Base, point T represents Third Base, point H represents Home Plate, and
point P represents another location on the baseball field.
The diagram has the following characteristics:
•
•
•
Quadrilateral FSTH is a square.
Point F lies on HP.
Triangle FST is isosceles.
a. What is the measure, in degrees, of
TFS? Show or explain how you got your answer.
b. What is the distance, in feet, between F and T? Show or explain how you got your answer.
A player caught a ball at point P.
c. What is the measure, in degrees, of
P? Show or explain how you got your answer.
d. What is the length, in feet, of FP ? Show or explain how you got your answer.
GEOMETRY
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38. Grade 10 | Mathematics | Open Response | 2009 | Question 41
Reporting Category: Geometry Standard(s): 10.G.7
Triangle MNP has vertices at M(0, 0), N(12, 0), and P(12, 16), as shown in the diagram below.
Let point R be the midpoint of MN. Let point S be the midpoint of NP.
a. What are the coordinates of each of the points listed below?
o point R
o point S
Show or explain how you got your answer for each point.
b. Is RS parallel to MP ? Show or explain how you got your answer.
c.
What is the length, in units, of each of the line segments listed below?
o MN
o NP
o MP
Show or explain how you got your answer for each line segment.
d. The length of MP is how many times the length of RS ? Show or explain how you got your answer.
GEOMETRY
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39. Grade 10 | Mathematics | Short Answer | 2005 | Question 19
Reporting Category: Geometry Standard(s): 10.G.3
In the figure shown below,
is parallel to
What is the measure of
?
, and
intersects
at Q.
GEOMETRY
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40. Grade 10 | Mathematics | Short Answer | 2006 | Question 16
Reporting Category: Geometry Standard(s): 10.G.6
Jeffrey wants to build a ramp to make it easier to load his lawn mower into the back of his truck. He drew the
diagram below to help him design the ramp.
Jeffrey's Ramp Design
What is t, the length in feet of the ramp?
GEOMETRY
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41. Grade 10 | Mathematics | Short Answer | 2007 | Question 16
Reporting Category: Geometry Standard(s): 10.G.4
Dan made an accurate scale drawing of the front of a building.
•
•
The width of the building in Dan's scale drawing is 5 inches.
The height of the building in his scale drawing is 3 inches.
If the actual width of the building is 100 feet, what is the actual height, in feet, of the building?
GEOMETRY
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42. Grade 10 | Mathematics | Multiple Choice | 2002 | Question 9
Reporting Category: Geometry Standard(s): 10.G.4
A landscape artist is designing two triangular flowerbeds so that:
•
•
•
•
LIM
PBC.
LIM encloses Flowerbed 1.
PBC encloses Flowerbed 2.
The measure of C is 50° and the measure of
What is the measure of
A. 50°
B. 55°
C. 75°
D. 105°
L?
B is 75°.
GEOMETRY
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43. Grade 10 | Mathematics | Multiple Choice | 2002 | Question 23
Reporting Category: Geometry Standard(s): 10.G.4
Isaac is going to draw
STU on the grid shown below so that it is congruent to
PQR.
He located point S at (–1, 0) and point T at (–4, 4). Which of the following coordinates represents a possible
location for point U?
A. (–3, 6)
B. (–3, 7)
C. (–4, 3)
D. (–4, 7)
GEOMETRY
44. Grade 10 | Mathematics | Multiple Choice | 2002 | Question 35
Reporting Category: Geometry Standard(s): 10.G.1
The lengths of three sides of a triangle are 5, 9, and x, all measured in centimeters.
What are all possible values of x?
A. 4 x 14
B. 0 x 14
C. 5 x 15
D. 3 x 9
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GEOMETRY
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45. Grade 10 | Mathematics | Multiple Choice | 2002 | Question 39
Reporting Category: Geometry Standard(s): 10.G.8
Which of the following equations represents a line that is parallel to the line 4x – 2y = 8 and passes through
the point (0, –8)?
A. 2x + y = –4
B. 2x – y = 8
C. x – 2y = 8
D. x – 2y = 16
GEOMETRY
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46. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 8
Reporting Category: Geometry Standard(s): 10.G.9
You may want to use the following coordinate plane to help you answer question 8.
As the result of a transformation, the image of the point (-1,3) is (-3,1). This is an example of a reflection
across the
A. line y = x.
B. line y = –x.
C. x-axis.
D. y-axis.
GEOMETRY
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47. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 17
Reporting Category: Geometry Standard(s): 10.G.6
Use the diagram below to answer question 17.
It is believed that the best angle to fly a kite is 45°. If you fly a kite at this angle and let out 225 feet of
string, approximately how high above the ground will the kite be?
A. 250 feet
B. 200 feet
C. 150 feet
D. 100 feet
GEOMETRY
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48. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 23
Reporting Category: Geometry Standard(s): 10.G.11
Use the map below to answer question 23.
Mr. Hendricks operates a snowplow for the Department of Public Works (D.P.W.). He found that he can
•
•
•
begin snowplowing at the D.P.W.
plow every street shown on the map above without going over any street more than once, and
end at his home.
Where is his home located?
A. at A
B. at B
C. at C
D. at D
GEOMETRY
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49. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 25
Reporting Category: Geometry Standard(s): 10.G.9
Use the graph below to answer question 25.
Suppose that
ABC is reflected over the x-axis. What are the coordinates of the image of point C?
A. (2,5)
B. (2,-5)
C. (-2,5)
D. (-2,-5)
GEOMETRY
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50. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 30
Reporting Category: Geometry Standard(s): 10.G.4
Use the figure below to answer question 30.
Which of the following statements gives enough additional information about the figure above to prove that
ABC is similar to EDC?
A.
BC
B.
BC
is the same length as
is twice as long as
EC
CD
C.
B is congruent to
D.
BCA is congruent to
D.
CED.
GEOMETRY
51. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 32
Reporting Category: Geometry Standard(s): 10.G.5
Use the triangle below to answer question 32.
What is the length x of the altitude of the triangle shown above?
A. 20 cm
B. 25 cm
C. 30 cm
D. 40 cm
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GEOMETRY
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52. Grade 10 | Mathematics | Multiple Choice | 2001 | Question 34
Reporting Category: Geometry Standard(s): 10.G.4
Use the triangle below to answer the question below.
In
ABC above,
A. 4.2
B. 6.0
C. 8.4
D. 7.0
MN
is parallel to
BC
. What is the length of
MN
?
GEOMETRY
53.
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Grade 10 | Mathematics | Multiple Choice | 2001 | Question 35
Reporting Category: Geometry Standard(s): 10.P.2
Use the graph below to answer question 35.
Point C on the graph above represents the distance and time that Catlyn traveled on her trip. Which of the
following represents her average speed?
A. x-coordinate of point C
B. y-coordinate of point C
C. slope of line through C and (0,0)
D. distance from the origin to point C
GEOMETRY
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54. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 6
Reporting Category: Geometry Objective(s):
A teacher makes the statement, "If all students pass this test, then there will be no homework on Friday."
Which of the following would indicate that the teacher did not follow through with this statement?
A. All of the students passed the test and they did not have homework on Friday.
B. All of the students did not pass the test and they had homework on Friday.
C. All of the students passed the test and they had homework on Friday.
D. All of the students did not pass the test and they did not have homework on Friday.
GEOMETRY
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55. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 9
Reporting Category: Geometry Objective(s):
The line l is a line of symmetry for figure MNOPQ. What is the measure
of NOP?
A. 70°
B. 110°
C. 140°
D. 160°
GEOMETRY
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56. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 15
Reporting Category: Geometry Objective(s):
If AD = BD = BC and the measure of
ABC?
A. 70°
B. 80°
C. 90°
D. 100°
ADB is twice the measure of
BDC, what is the measure of
GEOMETRY
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57. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 20
Reporting Category: Geometry Objective(s):
The lengths of three sides of a triangle are in the ratio of 3:4:5 and the perimeter of the triangle is 48 inches.
The length of the longest side of the triangle is
A. 15 inches.
B. 20 inches.
C. 25 inches.
D. 28 inches.
GEOMETRY
58. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 21
Reporting Category: Geometry Objective(s):
The spokes on the Ferris wheel are evenly spaced.
After 2
1
complete turns how many degrees will car M have traveled?
4
A. 90°
B. 225°
C. 450°
D. 810°
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GEOMETRY
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59. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 24
Reporting Category: Geometry Objective(s):
The diagram shows a carpenter's square that is used to measure riser height and tread length. A carpenter
has been asked to replace a staircase with one that is less steep. The carpenter could
A. increase the riser height leaving the tread length the same.
B. increase the tread length leaving the riser height the same.
C. increase the tread length and the riser height proportionally.
D. decrease the tread length and the riser height proportionally.
GEOMETRY
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60. Grade 10 | Mathematics | Multiple Choice | 1998 | Question 27
Reporting Category: Geometry Objective(s):
The ratio of the volume of a square pyramid with the dimension of the base y units on a side and 3y units
high,
y
compared to the volume of a square prism y units on a side and
units high
3
A. is greater than one.
B. is equal to one.
C. is less than one.
D. cannot be determined.
GEOMETRY
61.
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Grade 10 | Mathematics | Open Response | 2002 | Question 21
Reporting Category: Geometry Standard(s): 10.G.1
Alex wanted to find a pattern to predict the total number of diagonals in a convex polygon. He used each of
the figures below to determine the number of diagonals in the 4-sided convex polygon and the 5-sided
convex polygon shown below.
a. Create a table like the one shown below in your Student Answer Booklet. Complete the table to show
the relationship between the number of sides, the number of diagonals drawn from each vertex, and
the total number of diagonals in each of the convex polygons listed.
Number of sides
4 5 6 7 8
Number of diagonals from each vertex 1 2 3
Total number of diagonals
2 5 9
b. What is the total number of diagonals that a convex polygon of 12 sides has?
c.
Write an expression which represents the number of diagonals that a convex polygon of n sides has.
GEOMETRY
62.
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Grade 10 | Mathematics | Open Response | 1998 | Question 36
Reporting Category: Geometry Objective(s):
a. What is the area of waste (shaded area) after cutting the largest possible circular area from a 28" square
of sheet metal as shown in Figure 1? Show your work.
b. What is the area of waste (shaded area) after cutting the four largest possible circular areas from a 28"
square of sheet metal as shown in Figure 2? Show your work.
c. What general expression can you use to find the amount of waste when cutting n2 circles of equal size
from a square piece of sheet metal measuring 28" on a side?
GEOMETRY
(edited by Monteiro)
63. Grade 10 | Mathematics | Open Response | 1998 | Question 37
Reporting Category: Geometry Objective(s):
a. In your Student Answer Booklet, draw all of the possible lines of symmetry in each of the three triangles
below.
b. Write an if-then statement for each triangle below showing the relationship between the sides and the
lines of symmetry.
GEOMETRY
64.
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Grade 10 | Mathematics | Open Response | 1998 | Question 38
Reporting Category: Geometry Objective(s):
a. Using the patterns above, describe or draw the closed 3-dimensional figure that will be formed by
folding the patterns on the dashed lines. If it is not possible to make a closed 3-dimensional figure,
state the reason(s) why.
b. Make a pattern for a different closed 3-dimensional figure. Name and draw the geometric shape.
GEOMETRY
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65. Grade 10 | Mathematics | Short Answer | 2002 | Question 19
Reporting Category: Geometry Standard(s): 10.G.3
Use the figure below to answer the question.
Triangle ABC is inscribed in a circle O. What is the measure of
A?
GEOMETRY
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66. Grade 10 | Mathematics | Short Answer | 2001 | Question 11
Reporting Category: Geometry Standard(s): 10.G.7
In Oak Park, a picnic table is located 70 feet from the water fountain and 90 feet from the swings. What is the
longest possible distance that the water fountain could be from the swings?
GEOMETRY
67.
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Grade 10 | Mathematics | Short Answer | 2001 | Question 12
Reporting Category: Geometry Standard(s): 10.G.3
Runways A and B are parallel to each other and perpendicular to Runway C. If Runway D makes a 35° angle
with Runway A as shown in the diagram, what is the measure of the angle marked in the diagram between
Runways C and D?
GEOMETRY
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68. Grade 10 | Mathematics | Short Answer | 1998 | Question 28
Reporting Category: Geometry Objective(s):
A statement is made that two lines that intersect to form at least two congruent angles are perpendicular
lines. Draw a sketch that shows that the above statement is not always true.
GEOMETRY
69.
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Grade 10 | Mathematics | Short Answer | 1998 | Question 30
Reporting Category: Geometry Objective(s):
Jayne is surveying a piece of property. She needs to measure the distance across the pond from point A to
point B. She places a stake in the ground at point C. Then Jayne locates points D and E so that
ABC ~
EDC.
She measures BC, AC, CE, and DE as shown in the diagram.
Based on the data she has collected, what is the distance from A to B?
GEOMETRY
70. Grade 10 | Mathematics | Multiple Choice | 2010 | Question 8
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems
involving angles formed by transversals of coplanar lines. Identify and determine the
measure of central and inscribed angles and their association
Parallel lines r and s are cut by transversal t, as shown in the diagram below.
Which of the following must be true?
A.
B.
C.
D.
(edited by Monteiro)
GEOMETRY
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71. Grade 10 | Mathematics | Multiple Choice | 2010 | Question 13
Reporting Category: Geometry Standard(s): 10.G.9 - Draw the results, and interpret
transformations on figures in the coordinate plane, e.g., translations, reflections, rotations,
scale factors, and the results of success
Point P(6, 7) and point Q(6, 4) are plotted on the coordinate grid below.
Point P is rotated 180° clockwise about point Q. What are the coordinates of the image of point P
after this rotation?
A. (3, 4)
B. (6, 1)
C. (6, 10)
D. (9, 4)
GEOMETRY
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72. Grade 10 | Mathematics | Multiple Choice | 2010 | Question 22
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using
the triangle angle sum property and/or the Pythagorean theorem.
The diagram below shows a triangle and some of its dimensions.
What is the value of t?
A. 25
B. 30
C. 35
D. 40
GEOMETRY
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73. Grade 10 | Mathematics | Multiple Choice | 2010 | Question 35
Reporting Category: Geometry Standard(s): 10.G.6 - Use the properties of special triangles
(e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.
Gail drew square PQRS shown below.
What is the length, in inches, of
A.
B.
C.
D.
?
GEOMETRY
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74. Grade 10 | Mathematics | Multiple Choice | 2010 | Question 38
Reporting Category: Geometry Standard(s): 10.G.10 - Demonstrate the ability to visualize
solid objects and recognize their projections and cross sections.
The diagrams below show the top view and the front view of a solid object.
Which of the following could be a diagram of the solid object?
A.
B.
C.
D.
GEOMETRY
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75. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 39
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
The diagram below shows
. Point H lies on
Based on the angle measures in the diagram, what is
A. 21°
B. 42°
C. 55°
D. 76°
.
?
GEOMETRY
(edited by Monteiro)
76. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 35
Reporting Category: Geometry Standard(s): 10.G.1 - Identify figures using properties of sides,
angles, and diagonals. Identify the figures' type(s) of symmetry.
Which of the following is true for all parallelograms?
A. Diagonals are congruent.
B. Adjacent sides are congruent.
C. Opposite angles are congruent.
D. Adjacent angles are congruent.
GEOMETRY
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77. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 33
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
Pat is making a shelf for a corner in her house. The diagram below shows her plan for one piece she
will cut from a board.
Based on the dimensions in the diagram, what is the value of k?
A. 22
B. 26
C. 30
D. 34
GEOMETRY
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78. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 33
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
Two angles of a triangle each measure 64°. What is the measure of the third angle of the triangle?
A. 32°
B. 52°
C. 58°
D. 64°
GEOMETRY
79.
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Grade 10 | Mathematics | Multiple Choice | 2011 | Question 28
Reporting Category: Geometry Standard(s): 10.G.11 - Use vertex-edge graphs to model and
solve problems.
The diagram below represents different connecting routes an airplane pilot can take to travel from one
city to another.
An airplane will fly from Middletown to Wilton. The pilot of the airplane wants to stop in no more than 2
cities between Middletown and Wilton. How many different ways can the pilot fly from Middletown to
Wilton?
A. 1
B. 2
C. 3
D. 4
GEOMETRY
(edited by Monteiro)
80. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 28
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems involving
angles formed by transversals of coplanar lines. Identify and determine the measure of central
and inscribed angles and their association
In the diagram below, lines q and r are parallel lines intersected by line t.
Based on the diagram, which of the following equations must be true?
A.
B.
C.
D.
GEOMETRY
81.
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Grade 10 | Mathematics | Multiple Choice | 2011 | Question 22
Reporting Category: Geometry Standard(s): 10.G.4 - Apply congruence and similarity
correspondences (e.g.,
geometric figures.
In the diagram below,
ABC ≅
XYZ) and properties of the figures to find missing parts of
.
Based on the dimensions in the diagram, what is the length of
A. 3 in.
B. 4 in.
C. 5 in.
D. 6 in.
?
GEOMETRY
(edited by Monteiro)
82. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 22
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems involving
angles formed by transversals of coplanar lines. Identify and determine the measure of central
and inscribed angles.
In the diagram below, lines h and j are parallel. Line k and line m intersect lines h and j.
Based on the angle measures in the diagram, what is
A.
50°
B.
60°
C.
120°
D.
130°
?
GEOMETRY
(edited by Monteiro)
83. Grade 10 | Mathematics | Multiple Choice | 2011 | Question 1
Reporting Category: Geometry Standard(s): 10.G.7 - Using rectangular coordinates, calculate
midpoints of segments, slopes of lines and segments, and distances between two points, and
apply the results to the solutions of
In the diagram below, point M is the midpoint of
What are the coordinates of point J?
A. (-4, 1)
B. (-8, 2)
C. (-10, -4)
D. (-10, -8)
.
GEOMETRY
(edited by Monteiro)
84. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 23
Reporting Category: Geometry Standard(s): 10.G.7 - Using rectangular coordinates, calculate
midpoints of segments, slopes of lines and segments, and distances between two points, and
apply the results to the solutions of
Points M and H are shown on the coordinate grid below.
Point M is the midpoint of
A. (0, 1)
B. (2, 1)
C. (4, 2)
D. (12, 7)
. What are the coordinates of point G?
GEOMETRY
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85. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 24
Reporting Category: Geometry Standard(s): 10.G.1 - Identify figures using properties of sides,
angles, and diagonals. Identify the figures' type(s) of symmetry.
Two properties of a quadrilateral are listed below.
•
•
The quadrilateral always has 4 congruent angles.
The quadrilateral does not always have 4 congruent sides.
Which of the following quadrilaterals has both properties?
A. square
B. rhombus
C. rectangle
D. trapezoid
GEOMETRY
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86. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 26
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
The diagram below represents a ramp and some of its dimensions.
What is the height, h, of the ramp?
A. 1 ft.
B. 5 ft.
C. 8 ft.
D. 25 ft.
GEOMETRY
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87. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 27
Reporting Category: Geometry Standard(s): 10.G.6 - Use the properties of special triangles
(e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.
shown below,
In
What is
A. 25°
B. 50°
C. 65°
D. 80°
?
and
°.
GEOMETRY
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88. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 28
Reporting Category: Geometry Standard(s): 10.G.4 - Apply congruence and similarity
correspondences (e.g.,
geometric figures
In the diagram below,
ABC ≅
XYZ) and properties of the figures to find missing parts of
.
Based on the relationship between the triangles, which of the following proportions is true?
A.
B.
C.
D.
GEOMETRY
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89. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 30
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems involving
angles formed by transversals of coplanar lines. Identify and determine the measure of central
and inscribed angles
In the diagram below,
. Line w intersects lines m and q.
Which of the following are corresponding angles?
A.
B.
C.
D.
GEOMETRY
90.
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Grade 10 | Mathematics | Multiple Choice | 2012 | Question 30
Reporting Category: Geometry Standard(s): 10.G.9 - Draw the results, and interpret
transformations on figures in the coordinate plane, e.g., translations, reflections, rotations,
scale factors, and the results of success
Quadrilateral EFGH is shown on the coordinate grid below.
The quadrilateral will be reflected over the y-axis. The reflected image will then be translated 2 units
left and 7 units up. In which of the following quadrants will the final reflected and translated image
lie?
A. I and II
B. II and III
C. II and IV
D. III and IV
GEOMETRY
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91. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 32
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems involving
angles formed by transversals of coplanar lines. Identify and determine the measure of central
and inscribed angles
An angle is inscribed in a circle, as shown below.
The degree measures of three arcs are shown in the diagram. What is the value of x?
A. 55
B. 70
C. 75
D. 110
GEOMETRY
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92. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 35
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
The diagram below shows a triangle.
Based on the measurements in the diagram, what is k?
A. 8 ft.
B. 11 ft.
C. 12 ft.
D. 18 ft.
GEOMETRY
(edited by Monteiro)
93. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 37
Reporting Category: Geometry Standard(s): 10.G.1 - Identify figures using properties of sides,
angles, and diagonals. Identify the figures' type(s) of symmetry.
Which of the following could not be the exact number of right angles in a quadrilateral?
A. 1
B. 2
C. 3
D. 4
GEOMETRY
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94. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 38
Reporting Category: Geometry Standard(s): 10.G.5 - Solve simple triangle problems using the
triangle angle sum property and/or the Pythagorean theorem.
Point P and point Q are shown on the coordinate grid below.
Which of the following best represents the length of
A. 5 units
B. 6 units
C. 10 units
D. 14 units
?
GEOMETRY
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95. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 39
Reporting Category: Geometry Standard(s): 10.G.4 - Apply congruence and similarity
correspondences (e.g.,
geometric figures
Rectangle
ABC ≅
XYZ) and properties of the figures to find missing parts of
, as shown in the diagram below.
The area of rectangle KLMN is 12 square centimeters. Based on the dimensions in the diagram, what is the
length of
?
A. 9 cm
B. 10 cm
C. 15 cm
D. 24 cm
GEOMETRY
(edited by Monteiro)
96. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 39
Reporting Category: Geometry Standard(s): 10.G.3 - Recognize and solve problems involving
angles formed by transversals of coplanar lines. Identify and determine the measure of central
and inscribed angles and their asso
In the diagram below,
and
.
Based on the angle measure in the diagram, which of the following angles does not have a measure
of 62°?
A.
B.
C.
D.
GEOMETRY
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97. Grade 10 | Mathematics | Multiple Choice | 2012 | Question 40
Reporting Category: Geometry Standard(s): 10.G.6 - Use the properties of special triangles
(e.g., isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.
In the diagram below,
.
Based on the dimensions shown, what is the length of
A.
inches
B.
inches
C.
inches
D.
inches
?
GEOMETRY
(edited by Monteiro)
98. Grade 10 | Mathematics | Open Response | 2010 | Question 41
Reporting Category: Geometry Standard(s): 10.G.4 - Apply congruence and similarity
ABC ≅
correspondences (e.g.,
of geometric figures
XYZ) and properties of the figures to find missing parts
The diagram below shows
•
•
•
•
is an isosceles triangle with congruent sides
Point M lies on
, and point N lies on
is parallel to
The length of
c) What is
.
.
.
is 23 feet, and the length of
a) What is the length of
b) What is
and
is 10 feet.
? Show or explain how you got your answer.
? Show or explain how you got your answer.
? Show or explain how you got your answer.
d) Explain why
e) What is the length of
is similar to
.
? Show or explain how you got your answer.
GEOMETRY
99.
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Grade 10 | Mathematics | Open Response | 2011 | Question 20
Reporting Category: Geometry Standard(s): 10.G.9 - Draw the results, and interpret transformations on
figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of
success
Triangle JKL is shown on the coordinate plane below.
Copy the coordinate plane and triangle JKL as shown onto the grid in your Student Answer Booklet. Triangle
JKL is reflected over the y-axis.
a)
On your grid, draw triangle J′K′L′, the image of triangle JKL after it has been reflected over the yaxis. Be sure to label the vertices.
Triangle J′K′L′ is rotated 90° clockwise about the origin.
b)
On your grid, draw triangle J″K″L″, the image of J′K′L′ after it has been rotated 90° clockwise about
the origin. Be sure to label the vertices.
c)
Suppose the vertices of J″K″L″ are reflected over the y-axis and then reflected over the x-axis. Do
the vertices of the resulting triangle have the same coordinates as the vertices of triangle JKL? Show or
explain how you got your answer.
GEOMETRY
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100. Grade 10 | Mathematics | Open Response | 2011 | Question 20
Reporting Category: Geometry Standard(s): 10.G.6 - Use the properties of special triangles (e.g.,
isosceles, equilateral, 30°-60°-90°, 45°-45°-90°) to solve problems.
The diagram below shows
a)
b)
, its altitude
What is the degree measure of
, and some of its measurements.
? Show or explain how you got your answer.
For parts (b), (c), and (d), leave your answer as a square root of a number when appropriate.
c)
What is the length, in inches, of
? Show or explain how you got your answer.
d)
What is the length, in inches, of
? Show or explain how you got your answer.
e)
What is the length, in inches, of
? Show or explain how you got your answer.
GEOMETRY
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101. Grade 10 | Mathematics | Open Response | 2012 | Question 17
Reporting Category: Geometry Standard(s): 10.G.8 - Find linear equations that represent lines
either perpendicular or parallel to a given line and through a point, e.g., by using the "pointslope" form of the e
Line k passes through the points (4, 2) and (6, 5), as shown on the grid below.
a)
What is the slope of line k? Show or explain how you got your answer.
b)
What is the y-intercept of line k? Use the slope of line k to justify that your answer is correct.
c)
Write an equation that represents line k. Show or explain how you got your equation.
Line j has the following properties:
•
•
Line j is parallel to line k.
Line j passes through the point (2, 6).
d)
What is the slope of line j? Show or explain how you got your answer.
e)
Write an equation that represents line j. Show or explain how you got your equation.
GEOMETRY
(edited by Monteiro)
Answer Key
1)
A
11) B
21) A
31) D
41) 60
51) C
61) OR
2)
12) B
22) D
32) OR
42) B
52) A
62) OR
3)
B
13) B
23) B
33) OR
43) B
53) C
63) OR
4) C
14) A
24) D
34) OR
44) A
54) C
64) OR
5) D
15) D
25) C
35) OR
45) B
55) C
65) 40
6)
C
16) A
26) C
36) OR
46) B
56) C
66) 160
7) C
17) C
27) B
37) OR
47) C
57) B
67) 55
8) C
18) B
28) D
38) OR
48) D
58) D
68) SA
9) D
19) B
29) C
39) 80
49) D
59) B
69) 45.7
([45,46]
10) B
20) B
30) C
40) 5
50) C
60) A
70) B
C
GEOMETRY
(edited by Monteiro)
71)B
81)B
91)A
101) OR
111)
121)
131)
141)
72)A
82)C
92)C
102)
112)
122)
132)
142)
73)A
83)D
93)C
103)
113)
123)
133)
143)
74)C
84)A
94)C
104)
114)
124)
134)
144)
75)C
85)C
95)C
105)
115)
125)
135)
145)
76)C
86)B
96)A
106)
116)
126)
136)
146)
77)B
87)C
97)A
107)
117)
127)
137)
147)
78) B
88) A
98) OR
108)
118)
128)
138)
148)
79) D
89) A
99) OR
109)
119)
129)
139)
149)
80) D
90) B
100) OR
110)
120)
130)
140)
150)
GEOMETRY
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151)
161)
171)
181)
191)
201)
152)
162)
172)
182)
192)
202)
153)
163)
173)
183)
193)
203)
154)
164)
174)
184)
194)
204)
155)
165)
175)
185)
195)
205)
156)
166)
176)
186)
196)
206)
157)
167)
177)
187)
197)
207)
158)
168)
178)
188)
198)
208)
159)
169)
179)
189)
199)
209)
160)
170)
180)
190)
200)
210)
GEOMETRY
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