Geometry Post-Test Subject: Mathematics, Grade: 10, Year Created: 2017
Instructions
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Test
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1)
The coordinates for the endpoints of LM are L (-2, -3) and M (4, 5). LM is dilated by a scale factor of ( 1/ 2) from center of dilation (3, -2) to form
Segment L M . Which statement is not true?
Segment L M is parallel to Segment LM .
The length of Segment L M is twice the length of Segment LM .
The length of Segment L M is one-half the length of Segment LM .
The slope of Segment L M is the same as the slope of Segment LM .
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2)
The coordinates for the endpoints of Segment AB are A (1, 3) and B (5, 0). Segment AB is dilated by a scale factor of 3 with the origin as the
center of dilation to create Segment A B . Which of the following will be the slope of Segment A B ?
(3/ 4)
(4/ 3)
(- 3/ 4)
Slope of Segment A B cannot be determined from the information provided.
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3)
Howard draws two similar triangles.
How long is the third side of the smaller triangle?
8 centimeters
9 centimeters
22 centimeters
24 centimeters
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4)
Use the diagram to answer the question.
Zhan cut a drinking straw into three pieces (shown above) to investigate a triangle postulate. He moves the straw pieces to make triangles that
have been translated, rotated, and reflected from an original position. The end of one piece is always touching the end of another piece.
Which postulate could Zhan be investigating using only these straw pieces and no other tools?
The sum of the measures of the interior angles of all triangles is 180°.
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
The sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest side of a
triangle.
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles
are congruent.
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5)
Use the diagram to answer the question.
Daya is drawing a square inscribed in a circle using a compass and a
straightedge. Her first two steps are shown.
Which is the best step for Daya to do next?
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6)
Use the figures to answer the question.
Sasha derived the formula for the volume of a square pyramid. She started by
dividing a cube into 6 identical square pyramids. The top vertex of each pyramid
meets at the central point in the cube, with the cube’s diagonals as the edges.
V = the volume of a pyramid; s = side length of base, h = height of pyramid
The steps of Sasha’s work are shown.
Step 1: 6V= s 3
Step 2: V= ( 1/ 6) s 3
Maggie also derived the formula for volume of a square pyramid.
Maggie’s result is V= ( 1/ 3) s 2 h .
The formulas derived by Sasha and Maggie can both be used to correctly
calculate the volume of a square pyramid.
What are the best next steps for Sasha to take to prove that either formula can
be used to find the volume of a square pyramid?
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7)
Use the graph to answer the question.
(4, 4.6)
(4.5, 5)
(–5.5, –3)
(–5, –2.6)
Point G is drawn on the line segment so that the ratio of FG to GH is 5 to 1.
What are the coordinates of point G ?
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8)
Use the diagrams to answer the question.
Based on the two diagrams shown, which formula would be best to use to estimate the volume of City Park Pond?
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V= r 2 h
V= ( 1/ 3) Bh
V= ( 2/ 3) r 3
V= ( 1/ 3) r 2 h
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9)
Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. The zoo wants to
use one of Brittany’s designs but plans to change the volume of the cage.
Find the design change that would result in the birdcage with the greatest volume.
Increase the area of the base of the square pyramid by a factor of ten.
Increase the height of the cylinder by a factor of ten.
Increase the radius of the cone by a factor of ten.
Increase the radius of a sphere by a factor of ten.
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10)
Juan wants to build a greenhouse in his back yard. He needs to maximize the ratio of floor area to structure volume in order to provide the most
room for plants while minimizing the area to be heated.
Find the description of the structure that best meets Juan’s criteria.
A hemisphere with a diameter of 12 feet
A cube with a side length of 12 feet
A cone with a diameter of 12 feet and a height of 10 feet
A square pyramid with a base side length of 12 feet and a height of 9 feet
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11)
Use the graph and flow chart to answer the question.
Two non-vertical lines have the
same slope if and only if they
are parallel.
Angles supplementary to the
same angle or to congruent
angles are congruent.
If two parallel lines are cut by a
transversal, then each pair of
corresponding angles is
congruent.
Kamal dilates triangle ABC to get triangle A'B'C' . He knows that the triangles are similar because of the
definition of similarity transformations. He wants to demonstrate the angle-angle similarity postulate by
proving BAC B'A'C' and ABC A'B'C' . Kamal makes this incomplete flow chart proof.
What reason should Kamal add at all of the question marks in order to complete the proof?
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If two parallel lines are cut by a
transversal, then each pair of
alternate interior angles is
congruent.
12)
Jenna translated this triangle according to the rule ( x – 3, y
+ 2).
Which graph shows the result?
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13)
Kevin drew square WXYZ on this grid.
Kevin translated the square 3 units along the x- axis and -1 unit along the y -axis. What are the new coordinates
of the square?
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W' =
(-5, 3)
X'= (-1,
3)
Y'= (-1,
-1)
Z' = (-5,
-1)
W' =
(1, 1)
X' = (5, 1)
Y' = (5,
-3)
Z' =
(1, -3)
W' = (-3,
5)
X' = (1, 5)
Y' = (1, 1)
Z' = (-3,
1)
W' = (-1,
-1)
X' = (3,
-1)
Y' = (3,
-5)
Z' = (-1,
-5)
14)
Bella transformed triangle ABC to make triangle A'B'C'.
reflection over the x -axis
reflection over the y -axis
translation 2 units down
translation 4 units down
Which transformation did Bella use?
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15)
Triangle Q'R'S' is a translation of triangle QRS.
Which transformation created triangle Q'R'S'?
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translation 3 units left and 5 units up
translation 3 units right and 5 units down
translation 5 units left and 3 units up
translation 5 units right and 3 units down
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16)
Apply a dilation with a scale factor of 3 to triangle ABC. Let the image be triangle A’B’C’. Which one of the following equations is true?
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17)
Mr. Jones is trying to use a geometric shape to describe a tree trunk. Which shape would best describe a tree trunk?
a cylinder
a sphere
a cube
a cone
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18)
Bob is trying to describe a sphere to his little brother. Bob decides to go through his toys to find examples of spheres. Which of the following would
not be a good representation of a sphere?
a basketball
a baseball
a tennis ball
a football
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19)
Ron graphed 4 different lines that all had the same slope. Which statement correctly describes Ron’s lines?
None of the lines intersect each other.
Exactly 2 lines intersect each other.
Exactly 3 lines intersect each other.
All of the lines intersect each other.
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20)
The equation of line k is y = -
x–
. What is the equation of the line that is perpendicular to line k and passes through (0, 0)?
y = -8 x
y = -5 x
y=5x
y=8x
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21)
This graph represents the path of a ball rolling on a table.
y=1
y = -2
x=1
x = -2
A second ball rolls on the table parallel to the first ball. The path passes through (-2, 1). What is the equation of the path of the
second ball?
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22)
Use the diagram to answer the question.
The rectangle is rotated around the dashed line.
What three-dimensional shape shows the path of this rotation?
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23)
What is the name of the conic section shown by the shaded region?
circle
ellipse
parabola
hyperbola
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24)
Which shape could not be the intersection of a cone and a plane?
circle
ellipse
parabola
rectangle
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25)
A cone has a height of 45 centimeters and a radius of 6 centimeters. What is the best estimate for the volume of the cone?
300 cubic centimeters
600 cubic centimeters
1,700 cubic centimeters
4,200 cubic centimeters
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26)
A spherical marble has a diameter of 2 centimeters. What is the volume of the marble?
cubic centimeters
cubic centimeters
cubic centimeters
cubic centimeters
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27)
Lucy draws a line on a coordinate plane.
Which transformation will always result in a line perpendicular to Lucy’s line?
reflect over the line y = x
rotate 270° clockwise around the origin
reflect over the x -axis, and then reflect over the y -axis
dilate by a factor of 2 with the origin as the center of dilation
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28)
Use the graph to answer the question.
reflect over the line x = –3
reflect over the line y = –3
reflect over the line x = 3
reflect over the line y = 3
Which transformation carries the trapezoid onto itself?
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29)
What is the precise definition of an angle?
two rays that share a common endpoint
two line segments that share a common endpoint
the measure of an arc between two intersecting lines or line segments
one of the four intermediate spaces formed between two intersecting lines
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30)
Ethan transformed quadrilateral ABCD to make quadrilateral A'B'C'D'.
No, they are not congruent. ABCD was translated to form A'B'C'D'.
Yes, they are congruent. ABCD was translated to form A'B'C'D'.
No, they are not congruent. ABCD was reflected to form A'B'C'D'.
Yes, they are congruent. ABCD was reflected to form A'B'C'D'.
Are quadrilaterals ABCD and A'B'C'D' congruent? Why or why not?
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31)
Triangles ABC and DEF are similar.
What is the measure of angle C , rounded to the nearest tenth?
25.8°
42.0°
64.1°
90.0°
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32)
Triangle ABC is similar to triangle DEF .
What is the length of side FD ?
6 cm
12 cm
17 cm
18 cm
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33)
How are these two triangles related?
congruent by side-side-side
congruent by side-angle-side
congruent by angle-side-angle
similar but not congruent
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34)
Ms. Castille is about 6 feet tall. At 3:00 P.M. her shadow is 8 feet long and the tree’s shadow 20 is feet long.
About how tall is the tree?
15 feet
18 feet
22 feet
24 feet
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35)
What is the sine of angle x ?
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36)
Which fraction is equal to the cosine of x ?
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37)
This right triangle has side lengths r , s , and t .
What is the tangent of angle x ?
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38)
This list shows the lengths of the sides of a right triangle.
leg = 10 meters
leg = 3 x meters
hypotenuse = 26 meters
What is the value of x ?
4
8
12
14
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39)
Caleb draws triangle ABC on the coordinate grid. Then he transforms triangle ABC, producing triangle A'B'C'. Triangles ABC and A'B'C' are similar,
but not congruent.
Which transformation of triangle ABC could produce this result?
dilate by a factor of 3
reflect over the line y = x
rotate 180° around the origin
stretch vertically by a factor of 3
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40)
Use the diagram to answer the question.
The value of the tangent of angle x is defined as
.
Which fact makes it possible to define the tangent of an angle?
The sum of the interior angles of a triangle equals 180°.
The angle and side measurements of congruent right triangles are equal.
All right triangles that share one congruent acute angle are similar, and therefore have equal side ratios.
For all right triangles that share one congruent acute angle, the other acute angle is also congruent.
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41)
Armando designs a suspension bridge. He makes this drawing to show its size.
After the bridge is built, Armando is asked to design another bridge. The second bridge needs to have a similar shape to Armando’s first bridge, but
it only needs to be 184-feet long. How tall does the second bridge need to be?
32 feet
36 feet
40 feet
44 feet
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42)
A six-sided number cube has numbers 1, 2, 3, 4, 5 and 6. Which of the following is another way to describe the event of rolling an even number?
rolling a 2 or 4
rolling a 2 and 4 and 6
rolling a 1 or 3 or 5
not rolling a 1 or 3 or 5
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43)
Steps in Constructions
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44)
Select true statements if A and B are independent events
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45)
Select logs with greater than given weight
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46)
A pine tree farmer wants to estimate the volume of wood in his pine trees. If his average tree has a 3 foot diameter base, is 60 feet tall, and tapers
to a diameter of 2 inches near the top, which of the following would be used to model the tree?
cone
cylinder
square pyramid
rectangular prism
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47)
In the circle shown below r is the length of the radius and x is the measure of central angle ABC.
Which of the following would be used to find the area of the sector defined by central angle ABC?
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48)
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49)
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50)
The average length for the trunk of an adult elephant is 7 feet. Which of the following formulas could be used to best approximate the volume of an
adult elephant’s trunk?
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51)
A diagram for the entry chute to a stadium is shown below. Assume that all segments that appear to be parallel are parallel and that all segments
that appear to be perpendicular are perpendicular.
To determine the maximum occupancy of the chute, the fire department requires chute designers to allow 0.75 feet 2 for each person in the chute.
Which of the following would be the maximum occupancy of the chute at any given moment?
181 persons
235 persons
321 persons
408 persons
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52)
The side length of this square is x . What is the radius of the circle?
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53)
Segments AB and BC are tangent to circle P.
What is the value of x ?
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82°
92°
88°
98°
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54)
Segments CY and CZ are radii of circle C .
0.6 centimeters
1.4 centimeters
2.1 centimeters
2.8 centimeters
Chord WZ is 5.6 centimeters long. What is the length of XY ?
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55)
What is the length of y on this circle?
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8 units
12 units
10 units
18 units
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56)
Two circles have the same center. Circle P has a radius of p units. Circle Q has a radius of q units.
Which dilation could be used to prove that circles P and Q are similar?
Dilate circle P by a scale factor of
.
Dilate circle Q by a scale factor of
.
Dilate circle P by a scale factor of p × q .
Dilate circle Q by a scale factor of p × q .
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57)
Use the diagram to answer the question.
Angle AEC is inscribed in circle D . Angle ABC circumscribes circle D .
Which equation about the relationships in the circle is true ?
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58)
The location of point K after a translation is (-2, 3). Which rule describes this translation?
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( x – 3, y + 6)
( x , y + 6)
( x – 6, y + 3)
( x – 3, y )
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59)
Jerome reflected this figure over the line y = 2.
Which graph shows the result?
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60)
Jacob transformed quadrilateral FGHJ to F'G'H'J'.
reflection across the x -axis
reflection across the y -axis
reflection across the line x = 1
reflection across the line y = 1
Which transformation did Jacob use?
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