Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which statement is a counterexample for the following conditional?
If you
live in Springfield, then you live in Illinois.
a. | Sara Lucas lives in Springfield. | b. | Jonah Lincoln lives in Springfield,
Illinois. | c. | Billy Jones lives in Chicago, Illinois. | d. | Erin Naismith lives
in Springfield, Massachusetts. |
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2.
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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 |
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3.
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Which choice shows a true conditional with the hypothesis and conclusion
identified correctly?
a. | Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is
Thursday.
Conclusion: Yesterday was Monday. | b. | If tomorrow is Thursday, then yesterday was
Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not
Thursday. | c. | If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was
Tuesday.
Conclusion: Tomorrow is Thursday. | d. | Yesterday was Tuesday if tomorrow is
Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was
Tuesday. |
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4.
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Is the statement a good definition? If not, find a counterexample.
A square
is a figure with two pairs of parallel sides and four right angles.
a. | The statement is a good definition. | b. | No; a rhombus is a
counterexample. | c. | No; a rectangle is a counterexample. | d. | No; a parallelogram is a
counterexample. |
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5.
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Which statement provides a counterexample to the following faulty
definition?
A square is a figure with four congruent sides.
a. | A six-sided figure can have four sides congruent. | b. | Some triangles have
all sides congruent. | c. | A square has four congruent
angles. | d. | A rectangle has four sides. |
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6.
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Which statement is the Law of Detachment?
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7.
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Which statement is true?  a. |  are same-side angles. | b. |  are same-side angles. | c. |  are alternate interior
angles. | d. |  are alternate interior
angles. |
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8.
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Which is a correct two-column proof?
Given:  Prove:  and  are
supplementary. 
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9.
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 . Find the value of x for p to
be parallel to q. The diagram is not to scale. 
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10.
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Find the value of the variable. The diagram is not to scale.
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11.
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The jewelry box has the shape of a regular pentagon. It is packaged in a
rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to
fill its four corners. Find the measure of the foam angle marked. 
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12.
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The sum of the measures of two exterior angles of a triangle is 255. What is the
measure of the third exterior angle?
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13.
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Complete this statement. A polygon whose sides all have the same length is said
to be ____.
a. | regular | b. | equilateral | c. | equiangular | d. | convex |
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14.
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Graph  .
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15.
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Graph the line that goes through point (–5, 5) with slope  .
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16.
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Write an equation in slope-intercept form of the line through points
S(–10, –3) and T(–1, 1).
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17.
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At the curb a ramp is 11 inches off the ground. The other end of the ramp rests
on the street 55 inches straight out from the curb. Write a linear equation in slope-intercept form
that relates the height y of the ramp to the distance x from the curb.
a. | y =  x + 11 | c. | y =  x + 55 | b. | y =  x +
11 | d. | y =  x + 55 |
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18.
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What must be true about the slopes of two perpendicular lines, neither of which
is vertical?
a. | The slopes are equal. | b. | The slopes have product 1. | c. | The slopes have
product –1. | d. | One of the slopes must be
0. |
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19.
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a. | Symmetric Property of  ; SSS | c. | Reflexive Property of  ; SSS | b. | Reflexive Property of  ; SAS | d. | Symmetric Property of  ; SAS |
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20.
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State whether  and  are
congruent. Justify your answer.  a. | yes, by either SSS or SAS | b. | yes, by SSS only | c. | yes, by SAS
only | d. | No; there is not enough information to conclude that the triangles are
congruent. |
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21.
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a. | ASA Postulate | c. | SAS Postulate | b. | SSS Postulate | d. | AAS Theorem |
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22.
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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 |
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23.
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a. | ASA; Substitution | c. | AAS; CPCTC | b. | SAS; CPCTC | d. | ASA; CPCTC |
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24.
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What is the measure of the vertex angle of an isosceles triangle if one of its
base angles measures 42°?
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25.
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a. | I only | b. | II only | c. | I and II | d. | II and
III |
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26.
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Which statement can you conclude is true from the given
information? Given:  is the perpendicular bisector of   a. | AJ = BJ | c. | IJ = JK | b. | 
is a right angle. | d. | A
is the midpoint of  . |
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27.
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Three security cameras were mounted at the corners of a triangular parking lot.
Camera 1 was 158 ft from camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft apart.
Which camera had to cover the greatest angle?
a. | camera 2 | b. | camera 1 | c. | cannot tell | d. | camera
3 |
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28.
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Jay, Kay, and Ray found themselves far apart when they stopped for lunch while
working in a field. Jay could see Kay, then turn through 75° and see Ray. Kay could see Ray,
then turn through 50° and see Jay. Ray could see Jay, then turn through 55° and see Kay.
Which two were farthest apart?
a. | Kay and Ray | b. | Jay and Kay | c. | Ray and
Jay | d. | Kay and Ray were the same distance apart as Ray and
Jay. |
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29.
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Which three lengths could be the lengths of the sides of a triangle?
a. | 12 cm, 5 cm, 17 cm | c. | 9 cm, 22 cm, 11 cm | b. | 10 cm, 15 cm, 24 cm | d. | 21 cm, 7 cm, 6
cm |
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30.
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Two sides of a triangle have lengths 10 and 15. What must be true about the
length of the third side?
a. | less than 25 | b. | less than 10 | c. | less than 15 | d. | less than
5 |
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31.
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Two sides of a triangle have lengths 6 and 17. Which expression describes the
length of the third side?
a. | at least 11 and less than 23 | c. | greater than 11 and at most
23 | b. | at least 11 and at most 23 | d. | greater than 11 and less than 23 |
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32.
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Judging by appearance, classify the figure in as many ways as possible.  a. | rectangle, square, quadrilateral, parallelogram, rhombus | b. | rectangle, square,
parallelogram | c. | rhombus, trapezoid, quadrilateral, square | d. | square, rectangle,
quadrilateral |
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33.
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WXYZ is a parallelogram. Name an angle congruent to  
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34.
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Find values of x and y for which ABCD must be a
parallelogram. The diagram is not to scale.  a. | x = 10, y = 38 | b. | x = 10, y =
21 | c. | x = 10, y = 7 | d. | x = 7, y =
10 |
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35.
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Which description does NOT guarantee that a trapezoid is isoscles?
a. | congruent diagonals | b. | both pairs of base angles congruent
| c. | congruent bases | d. | congruent legs
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36.
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Which diagram shows the most useful positioning and accurate labeling of a kite
in the coordinate plane?
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37.
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If  , which equation must be true?
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38.
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Solve the extended proportion  for x and y
with x > 0 and y > 0. a. | x = 6; y = 6 | c. | x = 3; y =
12 | b. | x = 2; y = 18 | d. | x = 8; y = 24 |
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39.
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Figure  . Name a pair of corresponding sides? 
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Are the polygons similar? If they are, write a similarity statement and give
the similarity ratio.
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40.
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In DRST, RS = 10, RT = 15, and
mÐR = 32. In DUVW,
UV = 12, UW = 18, and mÐU = 32.
a. |  ;  | c. |  ;
 | b. |  ;
 | d. | The triangles are not
similar. |
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Explain why the triangles are similar. Then find the value of
x.
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41.
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a. | SSS Postulate;  | c. | SAS Postulate;  | b. | AA Postulate;  | d. | AA Postulate;  |
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42.
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Jason wants to walk the shortest distance to get from the parking lot to the
beach.  | a. | How far is the spot on the beach from the parking
lot? | | b. | How
far will his place on the beach be from the refreshment stand? | | |
a. | 24 m; 32 m | c. | 34 m; 16 m | b. | 38 m; 12 m | d. | 24 m; 18 m |
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Find the value of x. Round your answer to the nearest
tenth.
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43.
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a. | 6.2 cm | b. | 12.7 cm | c. | 15.5 cm | d. | 10.9
cm |
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Find the value of x. Round the length to the nearest tenth.
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44.
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a. | 7.6 ft | b. | 10.6 ft | c. | 15.3 ft | d. | 7.9
ft |
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45.
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An airplane over the Pacific sights an atoll at an angle of depression of 5  . At this time, the horizontal distance from the airplane to the atoll is 4629 meters.
What is the height of the plane to the nearest meter?  a. | 403 m | b. | 405 m | c. | 4611 m | d. | 4647
m |
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46.
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The vertices of a triangle are P(–2, –4), Q(2,
–5), and R(–1, –8). Name the vertices of the image reflected in the
y-axis.
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47.
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The vertices of a triangle are P(–7, –4), Q(–7,
–8), and R(3, –3). Name the vertices of the image reflected in the line y =
x.
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48.
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Describe in words the translation represented by the vector  . a. | 2 units to the right and 1 units down | b. | 1 units to the right and 2 units
down | c. | 2 units to the left and 1 units down | d. | 2 units to the left and 1 units
up |
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49.
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Use an ordered pair to describe the translation that is 7 units to the left and
1 units down.
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The hexagon GIKMPR and  FJN are regular.
The dashed line segments form 30° angles.
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50.
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Find the angle of rotation about O that maps  to  .
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51.
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Which type of isometry is the equivalent of two reflections across intersecting
lines?
a. | glide reflection | c. | reflection | b. | rotation | d. | none of these |
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52.
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Which letter has rotational symmetry?
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53.
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Which figure can be used to make a pure tessellation?
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54.
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Which tessellation has rotational symmetry and translational symmetry, but no
other types of symmetry?
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55.
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When designing a building, you must be sure that the building can withstand
hurricane-force winds, which have a velocity of 73 mi/h or more. The formula 
gives the force F in pounds exerted by a wind blowing against a flat surface. A is the
area of the surface in square feet, and v is the wind velocity in miles per hour. How much
force is exerted by a wind blowing at 81 mi/h against the side of the building shown?  a. | about 54 tons | c. | about 10,826 tons | b. | about 5 tons | d. | about 28 tons |
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56.
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The Ruffs are planning to buy an above-ground swimming pool shaped as a regular
octagon. The radius of the octagon is 9 feet. To the nearest tenth, find the area of the surface of
the water in the pool.
a. | 458.2 ft | b. | 553.1 ft | c. | 94.8 ft | d. | 229.1 ft |
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57.
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Grade 7 students were surveyed to determine how many hours a day they spent on
various activities. The results are shown in the circle graph below. Find the measure of each central
angle in the circle graph. a. Sleeping b. Eating  a. | 118.8°; 28.8° | b. | 108°;
28.8° | c. | 118.8°; 288° | d. | 59.4°; 288° |
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58.
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Identify a semicircle that contains C.  a. | semicircle ABC | c. | semicircle CB | b. | semicircle AC | d. | semicircle
ACB |
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Find the area of the circle. Leave your answer in terms of  .
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59.
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a. | 25.92 m2 | b. | 1.8
m2 | c. | 12.96 m2 | d. | 46.66
m2 |
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60.
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The figure represents the overhead view of a deck surrounding a hot tub. What is
the area of the deck? Round to the nearest tenth.  a. | 75.4 m2 | b. | 89.8 m2 | c. | 278.7 m2 | d. | 22.9
m2 |
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Short Answer
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61.
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Write the converse of the statement. If the converse is true, write true;
if not true, provide a counterexample.
If x = 4, then x2 = 16.
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62.
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Write the converse of the given true conditional and decide whether the converse
is true or false. If the converse is true, combine it with the conditional to form a true
biconditional. If the converse is false, give a counterexample.
If the probability that an
event will occur is 0, then the event is impossible to occur.
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63.
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Use the Law of Detachment to draw a conclusion from the two given statements. If
not possible, state not possible. Explain. Statement 1: If two lines intersect, then
they are not parallel. Statement 2:  do not intersect.
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64.
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For the given statements below, write the first statement as a conditional in
if-then form. Then, if possible, use the Law of Detachment to draw a conclusion from the two given
statements. If not possible, write not possible. Explain. A straight angle has a
measure of 180.  is a straight angle.
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Fill in each missing reason.
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65.
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66.
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67.
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Complete the paragraph proof. Given:  are
supplementary, and  are supplementary.
Prove: 
 By the definition of supplementary angles,
 _____ ( a) and  _____ ( b). Then  by
_____ ( c). Subtract  from each side. You get  _____ ( d), or  _____ ( e).
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68.
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A plumber knows that if you shut off the water at the main valve, it is safe to
remove the sink faucet. The plumber turns the main valve to the “Off” position. What
conclusion can the plumber make?
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69.
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Solve for x. Justify each step. 
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70.
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Write the conditional statement that the Venn diagram illustrates. 
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71.
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State the missing reasons in this proof.
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72.
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The 8 rowers in the racing boat stroke so that the angles formed by their oars
with the side of the boat all stay equal. Explain why their oars on either side of the boat remain
parallel.
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73.
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Find the measures of an interior angle and an exterior angle of a regular
polygon with 6 sides.
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74.
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Identify the form of the equation –3x – y = –2.
To graph the equation, would you use the given form or change to another form? Explain.
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75.
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The fireworks technician has two rocket launchers, each with a base and stand in
the form of an L. A diagonal trough on which the technician places a rocket joins the ends of each L.
One launcher has a 4-inch base and 10-inch stand. The other has a 6-inch base and a 15-inch stand.
Explain why two rockets launched from the two devices could follow parallel paths.
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76.
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For the two quadrilaterals below,    and  Complete this congruence statement for the
two quadrilaterals. 
___ ?___
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77.
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78.
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Based on the given information, can you conclude that  ?
Explain. Given:  ,  , and 
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79.
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Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that  . 
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80.
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81.
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Complete the statement  . Explain why it is
true. 
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82.
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Separate and redraw  and  . Identify
any common angles or sides. 
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83.
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Determine which triangles in the figure are congruent by AAS. 
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84.
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85.
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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. 
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86.
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In the figure,  ,  , and  .
Prove that  .
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87.
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For  and  ,  ,  , and  . Explain how
you can prove  by ASA.
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88.
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Can you conclude the triangles are congruent? Justify your answer. 
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89.
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90.
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Identify parallel segments in the diagram. 
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91.
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B is the midpoint of  and D is the
midpoint of  Solve for x, given  and  
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92.
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Complete the indirect proof.
Given: Bobby and Kina together hit at least 30 home runs. Bobby hit 18
home runs.
Prove: Kina hit at least 12 home runs.
Assume Kina hit a.___ than
12 home runs. This means Bobby and Kina combined to hit at most b.____ home runs. This
contradicts the given information that c. _____. The assumption is false. Therefore, Kina
d. ______.
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93.
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Complete the indirect proof.
Given: Rectangle JKLM has an area of 36 square centimeters.
Side  is at least 4 centimeters
long. Prove: KL £ 9 centimeters Assume that
a. ____. Then the area of rectangle JKLM is greater than b. _____ , which
contradicts the given information that c. _____. So the assumption must be false. Therefore,
d. _____.
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94.
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Can these three segments form the sides of a triangle? Explain. 
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95.
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Li went for a mountain-bike ride in a relatively flat wooded area. She rode for
6 km in one direction and then turned and pedaled 16 km in another. Finally she turned in the
direction of her starting point and rode 8 km. When she stopped, was it possible that Li was back at
her starting point? Explain.
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96.
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Find the values of the variables and the lengths of the sides of this rectangle.
The diagram is not to scale.
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97.
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What type of quadrilateral has exactly one pair of parallel sides?
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98.
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Isosceles trapezoid ABCD has legs  and  and base  If
AB = 4 y – 3, BC = 3 y – 4,
and CD = 5 y – 10, find the value of y.
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99.
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For parallelogram PQRS, find the values of x and y. Then
find PT, TR, ST, and TQ. The diagram is not to scale.
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100.
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Complete this statement: For parallelogram ABCD, 
Then state a definition or theorem that justifies your answer. 
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101.
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For A(1, –1), B(–1, 3), and C(4, –1),
find all locations of a fourth point, D, so that a parallelogram is formed using A,
B, C, D in any order as vertices. Plot each point D on a coordinate grid
and draw the parallelogram.
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102.
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Find the lengths of the diagonals of this trapezoid. 
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103.
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In the coordinate plane, draw a square with sides 4q units long. Give
coordinates for each vertex, and the coordinates of the point of intersection of the
diagonals.
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104.
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Judging by appearance, classify the figure in as many ways as possible using
rectangle, trapezoid, square, quadrilateral, parallelogram,
rhombus. 
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105.
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A highway makes an angle of 6  with the horizontal. This
angle is maintained for a horizontal distance of 8 miles. | a. | Draw and label a diagram to represent this
situation. | | b. | To the nearest hundredth of a mile, how high does the highway rise in this 8-mile section?
Show the steps you use to find the distance. | | |
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106.
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The diagram shows the locations of John and Mark in relationship to the top of a
tall building labeled A.  | a. | Describe 
as it relates to the situation. | | b. | Describe  as it relates to the situation. | | |
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107.
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A forest ranger spots a fire from a 21-foot tower. The angle of depression from
the tower to the fire is 12  . | a. | Draw a diagram to represent this
situation. | | b. | To the nearest foot, how far is the fire from the base of the tower? Show the steps you use
to find the solution. | | |
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For the vectors, (a) write the resultant as an ordered pair and (b) draw the
resultant.
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108.
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109.
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110.
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State whether the transformation appears to be an isometry. Explain. 
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111.
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In the diagram, the dashed figure is the image of the solid figure.  a. List all
pairs of corresponding sides. b. Name the image of point
 .
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112.
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Draw the image of  reflected in the x-axis. 
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113.
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Draw the image of the figure for a 52°
clockwise rotation about C. 
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114.
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Draw the image of the figure for the composition of a 90° rotation followed
by a 90° rotation about the origin. 
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115.
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Draw the image of the figure after you rotate the figure 45° about the
origin and then rotate it 135° about the origin.
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116.
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Draw the image of the figure after you rotate the figure 90° about (3, 3)
and then rotate it 180° about (0, 0).
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117.
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Does the tessellation have reflectional symmetry? Explain. 
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118.
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The dashed triangle is a dilation image of the solid triangle. Find the center
and scale factor of the dilation. 
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Use scalar multiplication to find the image vertices for a dilation with
center (0, 0) and the given scale factor.
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119.
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scale factor 4 
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120.
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The regular polygon has radius 9 m. Find each angle measure to the nearest tenth
of a degree, each linear measure to the nearest tenth of a meter, and the square measure to the
nearest square meter.  | a. |  | | b. |  | | c. | OX | | d. | AB | | e. | the perimeter | | f. | the area | | |
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