Name: ______________________ Class: _________________ Date: _________ ID: A

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Geometry Unit 1 Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Based on the pattern, what are the next two terms of the sequence?9, 15, 21, 27, . . .a. 33, 972 b. 39, 45 c. 162, 972 d. 33, 39

____ 2. Based on the pattern, what are the next two terms of the sequence?

5, 53

, 59

, 527

, 581

, . . .

a. 584

, 5246

c. 5243

, 5246

b. 5243

, 5729

d. 584

, 587

____ 3. Based on the pattern, what is the next figure in the sequence?

a. b. c. d.

____ 4. Find a counterexample to show that the conjecture is false.Conjecture: Any number that is divisible by 4 is also divisible by 8.a. 24 b. 40 c. 12 d. 26

____ 5. Find a counterexample to show that the conjecture is false.Conjecture: The product of two positive numbers is greater than the sum of the two numbers.a. 3 and 5b. 2 and 2c. A counterexample exists, but it is not shown above.d. There is no counterexample. The conjecture is true.

____ 6. Alfred is practicing typing. The first time he tested himself, he could type 23 words per minute. After practicing for a week, he could type 26 words per minute. After two weeks he could type 29 words per minute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice.a. 39 words per minute c. 35 words per minuteb. 29 words per minute d. 32 words per minute

Name: ______________________ ID: A

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____ 7. May’s Internet Services designs websites. May noticed an increase in her customers over a period of 5 consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number of customers May will have in the seventh week.

a. May will have 7 customers. c. May will have 11 customers.b. May will have 9 customers. d. May will have 13 customers.

____ 8. Are O, N, and P collinear? If so, name the line on which they lie.

a. No, the three points are not collinear. b. Yes, they lie on the line MP.c. Yes, they lie on the line NP.d. Yes, they lie on the line MO.

____ 9. Name the plane represented by the front of the box.

a. FBC b. BAD c. FEC d. FKG

Name: ______________________ ID: A

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____ 10. Are points B, J, and C collinear or noncollinear?

a. collinear b. noncollinear c. impossible to tell

____ 11. Name the line and plane shown in the diagram.

a. RS→←⎯⎯

and plane RSU c. RS→←⎯⎯

and plane UR

b. line R and plane RSU d. SR→←⎯⎯

and plane UT

____ 12. What is the intersection of plane TUYX and plane VUYZ?

a. UY→←⎯⎯

b. SW→←⎯⎯

c. TX→←⎯⎯

d. VZ→←⎯⎯

____ 13. Name the intersection of plane BPQ and plane CPQ.

a. PQ→←⎯⎯

c. CQ→←⎯⎯

b. BP→←⎯⎯

d. The planes need not intersect.

Name: ______________________ ID: A

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____ 14. Name a fourth point in plane TUW.

a. Y b. Z c. W d. X

____ 15. ____ two points are collinear.a. Any b. Sometimes c. No

____ 16. Plane ABC and plane BCE ____ be the same plane.a. must b. may c. cannot

____ 17. DE and CF ____ be coplanar.a. must b. may c. cannot

____ 18. Which diagram shows plane PQR and plane QRS intersecting only in QR→←⎯⎯

?

a. c.

b. d.

____ 19. Name the ray in the figure.

a. BA→⎯⎯

b. AB→←⎯⎯

c. BA d. AB→⎯⎯

Name: ______________________ ID: A

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____ 20. Name the ray that is opposite BA→⎯⎯

.

a. BD→⎯⎯⎯

b. BA→⎯⎯

c. CA→⎯⎯

d. DA→⎯⎯⎯

____ 21. Find AC.

a. 14 b. 15 c. 12 d. 4

____ 22. If EF = 2x − 12, FG = 3x − 15, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale.

a. x = 10, EF = 8, FG = 15 c. x = 10, EF = 32, FG = 45b. x = 3, EF = –6, FG = –6 d. x = 3, EF = 8, FG = 15

____ 23. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale.

a. x = 5, ST = 45 c. x = 10, ST = 60b. x = 5, ST = 60 d. x = 10, ST = 45

____ 24. Which point is the midpoint of AE?

a. D b. B c. not B, C, or D d. C

____ 25. Which angle is a right angle?a. c.

b. d.

Name: ______________________ ID: A

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____ 26. Judging by appearance, name an acute angle, an obtuse angle, and a right angle.

a. ∠W, ∠X, ∠V c. ∠U, ∠W, ∠Yb. ∠V, ∠Y, ∠W d. ∠U, ∠V, ∠Y

____ 27. If m∠EOF = 26 and m∠FOG = 38, then what is the measure of ∠EOG? The diagram is not to scale.

a. 64 b. 12 c. 52 d. 76

____ 28. If m∠BOC = 27 and m∠AOC = 47, then what is the measure of ∠AOB? The diagram is not to scale.

a. 74 b. 40 c. 20 d. 54

Name: ______________________ ID: A

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____ 29. If m∠DEF = 122, then what are m∠FEG and m∠HEG? The diagram is not to scale.

a. m∠FEG = 122, m∠HEG = 58 c. m∠FEG = 68, m∠HEG = 122b. m∠FEG = 58, m∠HEG = 132 d. m∠FEG = 58, m∠HEG = 122

____ 30. Name an angle supplementary to ∠EOD.

a. ∠BOC b. ∠BOE c. ∠DOC d. ∠BOA

____ 31. In the figure shown, m∠AED = 120. Which of the following statements is false?

Not drawn to scalea. m∠AEB = 60b. ∠BEC and ∠CED are adjacent angles.c. m∠BEC = 120d. ∠AED and ∠BEC are adjacent angles.

____ 32. Supplementary angles are two angles whose measures have sum ____.Complementary angles are two angles whose measures have sum ____.a. 90; 180 b. 90; 45 c. 180; 360 d. 180; 90

Name: ______________________ ID: A

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____ 33. Two angles whose sides are opposite rays are called ____ angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called ____ angles.a. vertical; adjacentb. adjacent; verticalc. vertical; supplementaryd. adjacent; complementary

____ 34. How are the two angles related?

a. vertical c. complementaryb. supplementary d. adjacent

____ 35. The complement of an angle is 25°. What is the measure of the angle?a. 75° b. 155° c. 65° d. 165°

____ 36. ∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5, and m∠JKL = x − 9. Find the measure of each angle.a. ∠DFG = 47, ∠JKL = 53 c. ∠DFG = 52, ∠JKL = 48b. ∠DFG = 47, ∠JKL = 43 d. ∠DFG = 52, ∠JKL = 38

____ 37. ∠1 and ∠2 are supplementary angles. m∠1 = x − 39, and m∠2 = x + 61. Find the measure of each angle.a. ∠1 = 79, ∠2 = 101 c. ∠1 = 40, ∠2 = 150b. ∠1 = 40, ∠2 = 140 d. ∠1 = 79, ∠2 = 111

____ 38. If ∠A and ∠B are supplementary angles and m∠A = 4m∠B, find m∠A and m∠B.a. 72, 18 b. 144, 36 c. 18, 72 d. 36, 144

Name: ______________________ ID: A

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____ 39. MO→⎯⎯⎯

bisects ∠LMN, m∠LMO = 8x − 23, and m∠NMO = 2x + 37. Solve for x and find m∠LMN. The diagram is not to scale.

a. x = 9, m∠LMN = 98 c. x = 10, m∠LMN = 114b. x = 9, m∠LMN = 49 d. x = 10, m∠LMN = 57

____ 40. MO→⎯⎯⎯

bisects ∠LMN, m∠LMN = 5x − 23, m∠LMO = x + 32. Find m∠NMO. The diagram is not to scale.

a. 61 b. 45.75 c. 91.5 d. 66

____ 41. SQ→⎯⎯

bisects ∠RST, and m∠RSQ = 3x − 9. Write an expression for ∠RST. The diagram is not to scale.

a. 6x – 9 b. 6x – 18 c. 3x – 9 d. 1.5x – 4.5

Name: ______________________ ID: A

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____ 42. Identify the hypothesis and conclusion of this conditional statement:If two lines intersect at right angles, then the two lines are perpendicular.a. Hypothesis: The two lines are perpendicular. Conclusion:

Two lines intersect at right angles.b. Hypothesis: Two lines intersect at right angles. Conclusion:

The two lines are perpendicular.c. Hypothesis: The two lines are not perpendicular. Conclusion:

Two lines intersect at right angles.d. Hypothesis: Two lines intersect at right angles. Conclusion:

The two lines are not perpendicular.

____ 43. Write this statement as a conditional in if-then form:All triangles have three sides.a. If a triangle has three sides, then all triangles have three sides.b. If a figure has three sides, then it is not a triangle.c. If a figure is a triangle, then all triangles have three sides.d. If a figure is a triangle, then it has three sides.

____ 44. 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.

____ 45. Draw a Draw a Venn diagram to illustrate this conditional:Cars are motor vehicles.a. c.

b. d.

Name: ______________________ ID: A

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____ 46. 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; conclusionb. hypothesis; conclusion; conditional d. hypothesis; conditional; conclusion

____ 47. A conditional can have a ____ of true or false.a. hypothesis b. truth value c. counterexample d. conclusion

____ 48. What is the conclusion of the following conditional?A number is divisible by 3 if the sum of the digits of the number is divisible by 3.a. The number is odd.b. The sum of the digits of the number is divisible by 3.c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.d. The number is divisible by 3.

____ 49. What is the converse of the following conditional?If a point is in the first quadrant, then its coordinates are positive.a. If a point is in the first quadrant, then its coordinates are positive.b. If a point is not in the first quadrant, then

the coordinates of the point are not positive.c. If the coordinates of a point are positive, then the point is in the first quadrant.d. If the coordinates of a point are not positive, then

the point is not in the first quadrant.

____ 50. What is the converse and the truth value of the converse of the following conditional?If an angle is a right angle, then its measure is 90.a. If an angle is not a right angle, then its measure is 90.

Falseb. If an angle is not a right angle, then its measure is not 90.

Truec. If an angle has measure 90, then it is a right angle.

Falsed. If an angle has measure 90, then it is a right angle.

True

____ 51. Which conditional has the same truth value as its converse?a. If x = 7, then x| | = 7.b. If a figure is a square, then it has four sides.c. If x – 17 = 4, then x = 21.d. If an angle has measure 80, then it is acute.

____ 52. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.If x = 3, then x2 = 9.a. If x2 = 9, then x = 3. True; x2 = 9 if and only if x = 3.b. If x2 = 3, then x = 9. Falsec. If x2 = 9, then x = 3. True; x = 3 if and only if x2 = 9.d. If x2 = 9, then x = 3. False

Name: ______________________ ID: A

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____ 53. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.If two lines are parallel, they do not intersect.If two lines do not intersect, they are parallel.a. One statement is false. If two lines do not intersect, they could be skew..b. One statement is false. If two lines are parallel, they may intersect twice.c. Both statements are true. Two lines are parallel if and only if they do not intersect.d. Both statements are true. Two lines are not parallel if and only if they do not

intersect.

____ 54. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.If an angle is a right angle, its measure is 90.If an angle measure is 90, the angle is a right angle.a. One statement is false. If an angle measure is 90, the angle may be a vertical angle.b. One statement is false. If an angle is a right angle, its measure may be 180.c. Both statements are true. An angle is a right angle if and only if its measure is 90.d. Both statements are true. The measure of angle is 90 if and only if it is not a right

angle.

____ 55. Write the two conditional statements that make up the following biconditional.I drink juice if and only if it is breakfast time.a. I drink juice if and only if it is breakfast time.

It is breakfast time if and only if I drink juice.b. If I drink juice, then it is breakfast time.

If it is breakfast time, then I drink juice.c. If I drink juice, then it is breakfast time.

I drink juice only if it is breakfast time.d. I drink juice.

It is breakfast time.

____ 56. When a conditional and its converse are true, you can combine them as a true ____.a. counterexample c. unconditionalb. biconditional d. hypothesis

____ 57. Use the Law of Detachment to draw a conclusion from the two given statements.

If two angles are congruent, then they have equal measures.

∠P and ∠Q are congruent.a. m∠P + m∠Q = 90 c. ∠P is the complement of ∠Q.b. m∠P = m∠Q d. m∠P ≠ m∠Q

____ 58. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.I can go to the concert if I can afford to buy a ticket.I can go to the concert.a. I can afford to buy a ticket.b. I cannot afford to buy the ticket.c. If I can go to the concert, I can afford the ticket.d. not possible

Name: ______________________ ID: A

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____ 59. Which statement is the Law of Detachment?a. If p → q is a true statement and q is true, then p is true.b. If p → q is a true statement and q is true, then q → p is true.c. If p → q and q → r are true, then p → r is a true statement.d. If p → q is a true statement and p is true, then q is true.

____ 60. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.Statement 1: If x = 3, then 3x – 4 = 5.Statement 2: x = 3a. 3x – 4 = 5 c. If 3x – 4 = 5, then x = 3.b. x = 3 d. not possible

____ 61. Use the Law of Syllogism to draw a conclusion from the two given statements.If a number is a multiple of 64,then it is a multiple of 8.If a number is a multiple of 8, then it is a multiple of 2.a. If a number is a multiple of 64, then it is a multiple of 2.b. The number is a multiple of 2.c. The number is a multiple of 8.d. If a number is not a multiple of 2, then the number is not a multiple of 64.

____ 62. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.If something weighs more than Jill’s car, then it is too heavy for the bridge.Smiley the Elephant weighs 2,150 pounds.a. Smiley is too heavy for the bridge.b. Smiley weighs more than Jill’s car.c. If Smiley weighs more than 2000 pounds, then Smiley is too heavy for the bridge.d. If Smiley weighs more than Jill’s car, then Smiley is too heavy for the bridge.

____ 63. Which statement is the Law of Syllogism?a. If p → q is a true statement and p is true, then q is true.b. If p → q is a true statement and q is true, then p is true.c. if p → q and q → r are true statements, then p → r is a true statement.d. If p → q and q → r are true statements, then r → p is a true statement.

Name: ______________________ ID: A

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Fill in each missing reason.

____ 64. Given: m∠PQR = x − 5, m∠SQR = x − 11, and m∠PQS = 100.Find x.

m∠PQR + m∠SQR = m∠PQS a. _____x – 5 + x – 11 = 100 b. Substitution Property

2x – 16 = 100 c. Simplify2x = 116 d. _____

x = 58 e . Division Property of Equality

a. Angle Addition Postulate; Subtraction Property of Equalityb. Protractor Postulate; Addition Property of Equalityc. Angle Addition Postulate; Addition Property of Equalityd. Protractor Postulate; Subtraction Property of Equality

Name: ______________________ ID: A

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____ 65. Given: 11x − 6y = −1; x = 8

Prove: 896

= y

11x − 6y = −1; x = 8 a. ________

88 − 6y = −1 b. ________

−6y = −89 c. ________

y = 896

d. ________

896

= y e. ________

a. a. Givenb. Symmetric Property of Equalityc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

c. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equality

b. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Symmetric Property of Equality

d. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Addition Property of Equalitye. Symmetric Property of Equality

____ 66. Name the Property of Equality that justifies the statement:If p = q, then p − r= q − r.a. Reflexive Property c. Symmetric Propertyb. Multiplication Property d. Subtraction Property

____ 67. Which statement is an example of the Addition Property of Equality?a. If p = q then p ⋅ s= q ⋅ s c. If p = q then p − s= q − sb. If p = q then p + s= q + s. d. p = q

____ 68. Name the Property of Congruence that justifies the statement:If XY ≅ WX, then WX ≅ XY.a. Symmetric Property c. Reflexive Propertyb. Transitive Property d. none of these

____ 69. Name the Property of Congruence that justifies the statement:If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C.a. Transitive Property c. Reflexive Propertyb. Symmetric Property d. none of these

Name: ______________________ ID: A

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Use the given property to complete the statement.

____ 70. Transitive Property of CongruenceIf CD ≅ EF and EF ≅ GH, then ______.a. EF ≅ GH c. CD ≅ GHb. EF ≅ EF d. CD ≅ EF

____ 71. Multiplication Property of EqualityIf 4x ÷ 2 = 4, then ______.a. 4 = 4x ⋅ 2 c. 4x = 8b. 4 = 4x ÷ 2 d. 4x ⋅ 2 = 8

____ 72. Substitution Property of EqualityIf y = 3 and 8x + y = 12, then ______.a. 8(3) − y = 12 c. 8x + 3 = 12b. 3 − y = 12 d. 8x − 3 = 12

____ 73. BD bisects ∠ABC. m∠ABC = 7x. m∠ABD = 3x + 25. Find m∠DBC.a. 50 b. 125 c. 75 d. 175

____ 74. What is the negation of this statement?Miguel’s team won the game.a. It was not Miguel’s team that won the game.b. Miguel’s team lost the game.c. Miguel’s team did not win the game.d. Miguel’s team did not play the game.

____ 75. What is the inverse of this statement?If he speaks Arabic, he can act as the interpreter.a. If he does not speak Arabic, he can act as the interpreter.b. If he speaks Arabic, he can’t act as the interpreter.c. If he can act as the interpreter, then he does not speak Arabic.d. If he does not speak Arabic, he can’t act as the interpreter.

Name: ______________________ ID: A

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____ 76. Write the conditional statement illustrated by this Venn diagram.

a. If an animal is a mammal, then it is a cow.b. If an animal is a cow, then it is a mammal.c. If an animal is a mammal, then it is not a cow.d. If an animal is a cow, then it is not a mammal.

____ 77. Write the contrapositive of the conditional statement illustrated by this Venn diagram.

a. If an animal is not a poodle, then it is a dog.b. If an animal is not a dog, then it is a poodle.c. If an animal is not a poodle, then it is not a dog.d. If an animal is not a dog, then it is not a poodle.