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Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which of the following is not an undefined term?
|
a. |
segment |
c. |
plane |
|
b. |
line |
d. |
point |
____ 2. Point B lies on between A and C. and . Find AC.
____ 3. Find the distance between the points (8, –2) and (3, 0).
____ 4. Which statement has a false truth value?
|
a. |
If a polygon is equilateral, then it is a regular polygon. |
|
b. |
If an angle is obtuse, then the angle measure is greater than 90 degrees. |
|
c. |
If two lines intersect twice, then they will form complementary angles. |
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d. |
If a pentagon has fewer than 5 sides, then the sides will be congruent. |
____ 5. Identify two lines in the diagram.
____ 6. Identify the line segments that are congruent in the diagram.
|
a. |
@ ; @ ; @ |
c. |
@ ; @ ; @ |
|
b. |
@ ; @ ; @ |
d. |
@ ; @ ; @ |
____ 7. Tell whether the lines and appear parallel, perpendicular, or skew.
|
a. |
skew |
b. |
perpendicular |
c. |
parallel |
____ 8. Use the diagram to tell whether the angles CSN and NSR are complementary, supplementary, or neither.
|
a. |
complementary |
b. |
neither |
c. |
supplementary |
____ 9. Tell whether and are only adjacent, adjacent and form a linear pair, or not adjacent.
|
a. |
adjacent and form a linear pair |
c. |
not adjacent |
|
b. |
only adjacent |
|
____ 10. Complete the conjecture.
The sum of two odd numbers is _____.
|
a. |
even |
c. |
sometimes odd, sometimes even |
|
b. |
odd |
d. |
even most of the time |
____ 11. Make a table of values for the rule when x is an integer from 1 to 6. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample?
|
a. |
The pattern appears to be an decreasing set of perfect squares.
generates a counterexample. |
|
b. |
The pattern appears to be a decreasing set of prime numbers.
generates a counterexample. |
|
c. |
The pattern appears to be a decreasing set of perfect squares.
generates a counterexample. |
|
d. |
The pattern appears to be an increasing set of perfect squares.
generates a counterexample. |
____ 12. For her birthday party, Kelly invited her friends to a nearby roller-skating rink. The area of the rectangular rink is 2,108 ft2, and the length is 68 ft. What is the width of the rink?
|
a. |
The width of the rink is 31 ft. |
c. |
The width of the rink is 34 ft. |
|
b. |
The width of the rink is 37 ft. |
d. |
The width of the rink is 40 ft. |
____ 13. Find the length of .
|
a. |
= 7.5 |
c. |
= –9.5 |
|
b. |
= 6.5 |
d. |
= –6.5 |
____ 14. Use the Distance Formula to find the distance, to the nearest tenth, from R(7, –7) to V(–2, –3).
|
a. |
0.0 units |
c. |
–5.0 units |
|
b. |
9.8 units |
d. |
2.4 units |
____ 15. Identify the hypothesis and conclusion of the conditional statement.
If it is raining then it is cloudy.
|
a. |
Hypothesis: It is raining.
Conclusion: It is cloudy. |
|
b. |
Hypothesis: It is cloudy.
Conclusion: It is raining. |
|
c. |
Hypothesis: Clouds make rain.
Conclusion: Rain does not make clouds. |
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d. |
Hypothesis: Rain and clouds happen together.
Conclusion: Rain and clouds do not happen together. |
____ 16. . Prove that .
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a. |
is given. From the diagram, and are alternate interior angles. So by the Converse of the Alternate Interior Angles Postulate, . |
|
b. |
is given. From the diagram, and are corresponding angles. So by the Converse of the Corresponding Angles Postulate, . |
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c. |
is given. From the diagram, and are corresponding angles. So by the Corresponding Angles Postulate, . |
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d. |
By the Converse of the Corresponding Angles Postulate, . From the diagram, . |
____ 17. If possible, use the data in the table to prove the conjecture false.
If an element is a metal, then it is a solid at 70°F.
|
Metal |
Melting Point (°F) |
|
Tungsten |
6192 |
|
Copper |
1984 |
|
Silver |
1763 |
|
Mercury |
-38 |
|
a. |
None of these metals is a counterexample to the conjecture.
|
|
b. |
Copper is a counterexample to the conjecture.
Its melting point, 1984 degrees, is greater than 70 degrees. |
|
c. |
Tungsten is a counterexample to the conjecture.
Its melting point, 6192 degrees, is greater than 70 degrees. |
|
d. |
Mercury is a counterexample to this conjecture.
Its melting point, -38 degrees, is less than 70 degrees. |
____ 18. Classify the polygon.
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a. |
nonagon |
c. |
pentagon |
|
b. |
hexagon |
d. |
heptagon |
____ 19. Classify the polygon, and tell whether it is a regular polygon.
|
a. |
heptagon; not regular |
c. |
hexagon; regular |
|
b. |
heptagon; regular |
d. |
hexagon; not regular |
____ 20. Determine the missing measure in the set of congruent polygons.
|
a. |
15 m |
c. |
17 m |
|
b. |
16 m |
d. |
22 m |
____ 21. Write the contrapositive of the statement, “If a state's capital is Denver, then the state is Colorado.”
|
a. |
If a state is Colorado, then its capital is not Denver. |
|
b. |
If a state is Colorado, then its capital is Denver. |
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c. |
If a state is not Colorado, then its capital is not Denver. |
|
d. |
If a state's capital is not Denver, then the state is not Colorado. |
____ 22. Graph the quadrilateral with the given vertices. Classify the quadrilateral. Give as many names as possible.
F(1, 2), G(3, 0), H(1, –2), J(–1, 0)
|
a. |
Parallelogram |
c. |
Parallelogram, rectangle, rhombus, square |
|
b. |
Parallelogram, rhombus |
d. |
Parallelogram, rectangle |
____ 23. Find the perimeter of the rectangle.
|
a. |
122.5 cm |
c. |
84 cm |
|
b. |
1751.75 cm |
d. |
168 cm |
____ 24. Write the definition as a biconditional.
An acute angle is an angle whose measure is less than .
|
a. |
An angle is acute if its measure is less than . |
|
b. |
An angle is acute if and only if its measure is less than . |
|
c. |
An angle’s measure is less than if it is acute. |
|
d. |
An angle is acute if and only if it is not obtuse. |
____ 25. Use a truth table to assess the truth value of the conjunction of these statements:
p : A rhombus has four congruent sides.
q : The sum of the measures of the angles of a triangle is .
|
a. |
Since p is true, the conjunction is true. |
|
b. |
Since q is true, the conjunction is true. |
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c. |
Since p and q are true, the conjunction is true. |
|
d. |
Since q is false, the conjunction is false. |
____ 26. What is the area of a triangle with a base of 4 feet and a height of 12 feet?
____ 27. Which of the following is a counterexample to the following conjecture? If , then .
____ 28. Which statement has a true converse?
|
a. |
If two angles are complementary, then they are not supplementary. |
|
b. |
If an angle measures , then it is a right angle. |
|
c. |
If a polygon is a rectangle, then it is also a parallelogram. |
|
d. |
If two lines are perpendicular, then they intersect. |
|
e. |
None correct |
Use the diagram from the following problems.
____ 29. If , which length could be used to prove using the SAS Similarity Theorem?
|
a. |
EI = 3.2 |
d. |
EI = 6.4 |
|
b. |
HI = 13.2 |
e. |
None correct |
|
c. |
HI = 6.6 |
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____ 30. Identify the radii shown in circle W.
____ 31. Solve the equation . Fill in the missing justifications.
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|
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Given |
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[1] |
|
|
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Simplify. |
|
|
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[2] |
|
|
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Simplify. |
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a. |
[1] Substitution Property of Equality;
[2] Division Property of Equality |
|
b. |
[1] Addition Property of Equality;
[2] Division Property of Equality |
|
c. |
[1] Division Property of Equality;
[2] Subtraction Property of Equality |
|
d. |
[1] Addition Property of Equality;
[2] Reflexive Property of Equality |
____ 32. Simplify the expression. Justify each step. Fill in the missing justifications.
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|
|
|
|
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= |
[1] |
|
|
= |
[2] |
|
|
= |
Simplify. |
|
|
= |
|
|
a. |
[1] Identity Property of Addition
[2] Associative Property of Addition |
|
b. |
[1] Commutative Property of Addition
[2] Associative Property of Addition |
|
c. |
[1] Associative Property of Addition
[2] Commutative Property of Addition |
|
d. |
[1] Commutative Property of Addition
[2] Identity Property of Addition |
____ 33. Determine whether the triangles are congruent.
|
a. |
not congruent |
b. |
congruent |
____ 34. . and are equilateral. and . Find the total distance from A to B to C to D to E.
____ 35. Identify the property that justifies the statement.
and . So .
|
a. |
Reflexive Property of Equality |
c. |
Symmetric Property of Congruence |
|
b. |
Symmetric Property of Equality |
d. |
Transitive Property of Congruence |
____ 36. The baseball diamond at a playground is a square with sides that measure 60 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth.
|
a. |
120 feet |
c. |
60 feet |
|
b. |
84.9 feet |
d. |
7,200 feet |
____ 37. Complete the following proof of the Angle-Angle-Side Congruence Theorem.
Given:
Prove:
Proof:
|
Statements |
Reasons |
|
1. |
1. Given |
|
2. |
2. [1] |
|
3. |
3. Given |
|
4. |
4. [2] |
|
a. |
[1] ASA
[2] Third Angle Theorem |
c. |
[1] Third Angle Theorem
[2] ASA |
|
b. |
[1] Third Angle Theorem
[2] SAS |
d. |
[1] Given
[2] Third Angle Theorem |
____ 38. Given: , ,
Prove: DMLP is isosceles.
Complete the proof.
Proof:
|
Statements |
Reasons |
|
1. , |
1. Given |
|
2. |
2. Given |
|
3. |
3. Definition of congruent line segments |
|
4. |
4. Reflexive Property of Equality |
|
5. |
5. Subtraction Property of Equality |
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6. and |
6. Segment Addition Postulate |
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7. |
7. Substitute |
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8. DMLN DPLO |
8. [1] |
|
9. |
9. [2] |
|
10. DMLP is isosceles. |
10. Definition of isosceles triangle |
|
a. |
[1] CPCTC
[2] ASA |
c. |
[1] CPCTC
[2] AAS |
|
b. |
[1] ASA
[2] CPCTC |
d. |
[1] AAS
[2] CPCTC |
____ 39. Using the information about John, Jason, and Julie, can you uniquely determine how they stand with respect to each other? On what basis?
Statement 1: John and Jason are standing 12 feet apart.
Statement 2: The angle from Julie to John to Jason measures 31°.
Statement 3: The angle from John to Jason to Julie measures 49°.
|
a. |
No. There is no unique configuration. |
|
b. |
Yes. They form a unique triangle by SAS. |
|
c. |
Yes. They form a unique triangle by ASA. |
|
d. |
Yes. They form a unique triangle by SSS. |
____ 40. Find the measure of each interior angle of a regular 40-gon.
|
a. |
189 |
c. |
171 |
|
b. |
175.5 |
d. |
162 |
____ 41. Use the given paragraph proof to write a two-column proof.
Given: is a right angle.
Prove: are complementary.
Paragraph proof:
Since is a right angle, m by the definition of a right angle. By the Angle Addition Postulate, . By substitution, . Since , by the definition of congruent angles. Using substitution, . Thus, by the definition of complementary angles, are complementary.
Complete the proof.
Two-column proof:
|
Statements |
Reasons |
|
1. is a right angle. |
1. Given |
|
2. m |
2. Definition of a right angle |
|
3. |
3. [1] |
|
4. |
4. Substitution |
|
5. |
5. [2] |
|
6. |
6. Substitution |
|
7. are complementary. |
7. Definition of complementary angles |
|
a. |
[1] Substitution
[2] Definition of congruent angles |
c. |
[1] Angle Addition Postulate
[2] Definition of equality |
|
b. |
[1] Angle Addition Postulate
[2] Definition of congruent angles |
d. |
[1] Substitution
[2] Definition of equality |
____ 42. Given: Q is a right angle in the isosceles DPQR. X is the midpoint of . Y is the midpoint of .
Prove: DQXY is isosceles.
Complete the paragraph proof.
Proof: Draw a diagram and place the coordinates of DPQR and DQXY as shown.
By [2], the coordinates of X are and
the coordinates of Y are .
By [5],
Since , by definition. So DQXY is isosceles.
|
a. |
[1] a
[2] the Distance Formula
[3] , [4]
[5] the Midpoint Formula
[6] , [7]
|
c. |
[1] a
[2] the Midpoint Formula
[3] , [4]
[5] the Distance Formula
[6] , 7] |
|
b. |
[1] 2a
[2] the Distance Formula
[3] a, [4] a
[5] the Midpoint Formula
[6] a, [7] a |
d. |
[1] 2a
[2] the Midpoint Formula
[3] a, [4] a
[5] the Distance Formula
[6] a, [7] a |
____ 43. Tell whether the given side lengths form a right triangle.
5, 7, 10
____ 44. Two vertices of a parallelogram are A(2, 3) and B(8, 11), and the intersection of the diagonals is . Find the coordinates of the other two vertices.
|
a. |
(12, 9), (6, 1) |
c. |
(11, 8), (5, 0) |
|
b. |
, |
d. |
, |
____ 45. Find the length of arc with measure 100° in a circle with radius 2 in. Round to the nearest tenth.
____ 46. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
|
a. |
, HL |
c. |
, SAS |
|
b. |
, HL |
d. |
, SAS |
____ 47. The equations of four lines are given. Identify the perpendicular lines.
Line 1:
Line 2:
Line 3:
Line 4:
|
a. |
Lines 1 and 3 are perpendicular; Lines 2 and 4 are perpendicular. |
|
b. |
Lines 1 and 3 are perpendicular. |
|
c. |
None of the lines are perpendicular. |
|
d. |
Lines 2 and 4 are perpendicular. |
____ 48. Find the area of the composite figure.
|
a. |
216 ft2 |
c. |
378 ft2 |
|
b. |
297 ft2 |
d. |
540 ft2 |
____ 49. A homeowner wants to make a new deck for her backyard. Redwood costs $10 per square foot. The units on the graph are in feet. How much will it cost to create the deck shown?
|
a. |
$320 |
c. |
$400 |
|
b. |
$76 |
d. |
$380 |
____ 50. Complete the proof.
Given:
Prove:
Proof:
|
Statements |
Reasons |
|
1. |
1. Given |
|
2. |
2. Reflexive Property of Congruence |
|
3. [1] |
3. Angle Addition Postulate |
|
4. |
4. [2] |
|
5. |
5. [3] |
|
a. |
[1]
[2] Comparison Property of Inequality
[3] Hinge Theorem |
c. |
[1]
[2] Comparison Property of Inequality
[3] Converse of the Hinge Theorem |
|
b. |
[1]
[2] Hinge Theorem
[3] Comparison Property of Inequality |
d. |
[1]
[2] Converse of the Hinge Theorem
[3] Comparison Property of Inequality |
____ 51. Suppose and . If , what is ?
|
a. |
132° |
c. |
90° |
|
b. |
42° |
d. |
48° |
____ 52. Which congruence theorem applies to these triangles?
|
a. |
HL Congruence Theorem |
c. |
LA Congruence Theorem |
|
b. |
HA Congruence Theorem |
d. |
LL Congruence Theorem |
____ 53. Find a line that is parallel to and passes through point (4, 1).
____ 54. Which line is parallel to ?
|
a. |
|
d. |
|
|
b. |
|
e. |
None correct |
|
c. |
|
|
____ 55. Triangles AEB and DEF are similar by which of the following postulates?
|
a. |
AA Similarity Postulate |
c. |
SSS Similarity Postulate |
|
b. |
SAS Similarity Postulate |
d. |
These triangles are not similar. |
____ 56. What is the measure of the inscribed angle if its intercepted arc measure 92°?
|
a. |
184° |
c. |
92° |
|
b. |
46° |
d. |
88° |
____ 57. Identify the pairs of congruent angles and proportional corresponding side lengths.
|
a. |
, , , |
|
b. |
, , , |
|
c. |
, , , |
|
d. |
, , , |
____ 58. Identify the chords shown in circle E.
____ 59. Identify the secant that intersects .
____ 60. The plans for a new community include a rectangular park that has a perimeter of 600 ft. Dionne creates a model so that the similarity ratio of the model to the park is . What is the perimeter of the model in inches?
|
a. |
300,000 in. |
c. |
1 in. |
|
b. |
14.4 in. |
d. |
7,200 in. |
____ 61. Find .
|
a. |
= 9° |
c. |
= 18° |
|
b. |
= 46° |
d. |
= 36° |
____ 62. A wheel from a motor has springs arranged as in the figure. Find m .
|
a. |
m = |
c. |
m = |
|
b. |
m = |
d. |
m = |
____ 63. State the assumption you would make to start an indirect proof that is an obtuse angle.
|
a. |
assume is an acute angle |
c. |
assume is an obtuse angle |
|
b. |
assume is not an obtuse angle |
d. |
assume is not an acute angle |
____ 64. Write an indirect proof that an obtuse triangle does not have a right angle.
Given: is an obtuse triangle.
Prove: does not have a right angle.
Let be an obtuse angle. Assume has a right angle. Let be a right angle.
Use direct reasoning to lead to a contradiction.
Complete the proof.
|
|
[1] |
|
|
Sum of the interior s of a are |
|
|
Substitute for m . |
|
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