Geometry Unit 1 Review - RMHS - Mathematics
Name:Class:Date:ID: AGeometry Unit 1 ReviewMultiple 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, 972b. 39, 45c. 162, 972d.2. Based on the pattern, what are the next two terms5 5 555, , ,,,.3 9 27 8155a.,c.84 24655b.,d.243 729of the sequence?55,243 24655,84873. Based on the pattern, what is the next figure in the sequence?a.33, 39b.c.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. 24b. 40c. 12d.d.265. 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. Afterpracticing for a week, he could type 26 words per minute. After two weeks he could type 29 words perminute. Based on this pattern, predict how fast Alfred will be able to type after 4 weeks of practice.a. 39 words per minutec. 35 words per minuteb. 29 words per minuted. 32 words per minute1
Name:7. May’s Internet Services designs websites. May noticed an increase in her customers over a period of 5consecutive weeks. Based on the pattern shown in the graph, make a conjecture about the number ofcustomers May will have in the seventh week.a.b.May will have 7 customers.May will have 9 customers.c.d.May will have 11 customers.May will have 13 customers.8. Are O, N, and P collinear? If so, name the line on which they lie.a.b.c.d.ID: ANo, the three points are not collinear.Yes, they lie on the line MP.Yes, they lie on the line NP.Yes, they lie on the line MO.9. Name the plane represented by the front of the box.a.FBCb.BADc.2FECd.FKG
Name:ID: A10. Are points B, J, and C collinear or noncollinear?a.collinearb.noncollinearc.impossible to tell11. Name the line and plane shown in the diagram.a.b. RS and plane RSUc.line R and plane RSUd. RS and plane UR SR and plane UT12. What is the intersection of plane TUYX and plane VUYZ?a. UYb. SWc. TXd. VZ13. Name the intersection of plane BPQ and plane CPQ.a.b. PQ BPc.d.3 CQThe planes need not intersect.
Name:ID: A14. Name a fourth point in plane TUW.a.Yb.Z15. two points are collinear.a. Anyb.c.WSometimesd.c.No16. Plane ABC and plane BCE be the same plane.a. mustb. mayc.cannot17. DE and CF be coplanar.a. mustb.c.cannotmayX 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. BAb. ABc.4BAd. AB
Name:ID: A 20. Name the ray that is opposite BA .a. BDb. BAc.15c. CAd.12d. DA21. Find AC.a.14b.422. 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.b.x 10, EF 8, FG 15x 3, EF –6, FG –6c.d.x 10, EF 32, FG 45x 3, EF 8, FG 1523. If T is the midpoint of SU, find the values of x and ST. The diagram is not to scale.a.b.x 5, ST 45x 5, ST 60c.d.x 10, ST 60x 10, ST 45Bc.not B, C, or D25. Which angle is a right angle?a.c.24. Which point is the midpoint of AE?a.b.Db.d.5d.C
Name:ID: A26. Judging by appearance, name an acute angle, an obtuse angle, and a right angle.a.b. W, X, V V, Y, Wc.d. U, W, Y U, V, Y27. If m EOF 26 and m FOG 38, then what is the measure of EOG? The diagram is not to scale.a.64b.12c.52d.7628. If m BOC 27 and m AOC 47, then what is the measure of AOB? The diagram is not to scale.a.74b.40c.620d.54
Name:ID: A29. If m DEF 122, then what are m FEG and m HEG? The diagram is not to scale.a.b.m FEG 122, m HEG 58m FEG 58, m HEG 132c.d.m FEG 68, m HEG 122m FEG 58, m HEG 122c. DOC30. Name an angle supplementary to EOD.a. BOCb. BOEd. BOA31. In the figure shown, m AED 120. Which of the following statements is false?a.b.c.d.Not drawn to scalem AEB 60 BEC and CED are adjacent angles.m BEC 120 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; 180b. 90; 45c. 180; 360d.7180; 90
Name:ID: A33. Two angles whose sides are opposite rays are called angles. Two coplanar angles with a commonside, a common vertex, and no common interior points are called angles.a. vertical; adjacentb. adjacent; verticalc. vertical; supplementaryd. adjacent; complementary34. How are the two angles adjacent35. 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 ofeach angle.a. DFG 47, JKL 53c. DFG 52, JKL 48b. DFG 47, JKL 43d. DFG 52, JKL 3837. 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 101c. 1 40, 2 150b. 1 40, 2 140d. 1 79, 2 11138. If A and B are supplementary angles and m A 4m B, find m A and m B.a. 72, 18b. 144, 36c. 18, 72d. 36, 1448
Name:ID: A 39. MO bisects LMN, m LMO 8x 23, and m NMO 2x 37. Solve for x and find m LMN. Thediagram is not to scale.a.b.x 9, m LMN 98x 9, m LMN 49c.d.x 10, m LMN 114x 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.61b.45.75c.91.5d.66 41. SQ bisects RST, and m RSQ 3x 9. Write an expression for RST. The diagram is not to scale.a.6x – 9b.6x – 18c.93x – 9d.1.5x – 4.5
Name:ID: A42. 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.10
Name:ID: A46. Another name for an if-then statement is a . Every conditional has two parts. The part following ifis the and the part following then is the .a. conditional; conclusion; hypothesisc. conditional; hypothesis; conclusionb. hypothesis; conclusion; conditionald. hypothesis; conditional; conclusion47. A conditional can have a of true or false.a. hypothesisb. truth valuec.counterexampled.conclusion48. 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, thenthe 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, thenthe 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.True51. 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, combinethe 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. False11
Name:ID: A53. Determine whether the conditional and its converse are both true. If both are true, combine them as abiconditional. 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 notintersect.54. Determine whether the conditional and its converse are both true. If both are true, combine them as abiconditional. 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 rightangle.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. counterexamplec. unconditionalb. biconditionald. hypothesis57. 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 90b. m P m Qc.d. P is the complement of Q.m P m Q58. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, writenot 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 possible12
Name:ID: A59. 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 notpossible, write not possible.Statement 1: If x 3, then 3x – 4 5.Statement 2: x 3a. 3x – 4 5c. If 3x – 4 5, then x 3.b. x 3d. not possible61. 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 givenstatements.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 qb. If p q is a true statement and q is true, then pc. if p q and q r are true statements, then pd. If p q and q r are true statements, then r13is true.is true. r is a true statement. p is a true statement.
Name:ID: AFill 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 PQSx – 5 x – 11 1002x – 16 1002x 116x 58a.b.c.d.a.b. Substitution Propertyc. Simplifyd.e . Division Property of EqualityAngle Addition Postulate; Subtraction Property of EqualityProtractor Postulate; Addition Property of EqualityAngle Addition Postulate; Addition Property of EqualityProtractor Postulate; Subtraction Property of Equality14
Name:ID: A65. Given: 11x 6y 1; x 8Prove:89 y611x 6y 1; x 8a.88 6y 1b. 6y 89c.896d.y 89 ye.6a. a. Givenb. Symmetric Property of Equalityc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equalityb. a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Symmetric Property of Equalityc.d.a. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Division Property of Equalitye. Reflexive Property of Equalitya. Givenb. Substitution Propertyc. Subtraction Property of Equalityd. Addition Property of Equalitye. Symmetric Property of Equality66. Name the Property of Equality that justifies the statement:If p q, then p r q r.a. Reflexive Propertyc. Symmetric Propertyb. Multiplication Propertyd. Subtraction Property67. Which statement is an example of the Addition Property of Equality?a. If p q then p s q sc. If p q then p s q sb. If p q then p s q s.d. p q68. Name the Property of Congruence that justifies the statement:If XY WX, then WX XY.a. Symmetric Propertyc. Reflexive Propertyb. Transitive Propertyd. none of these69. Name the Property of Congruence that justifies the statement:If A B and B C, then A C.a. Transitive Propertyc. Reflexive Propertyb. Symmetric Propertyd. none of these15
Name:ID: AUse the given property to complete the statement.70. Transitive Property of CongruenceIf CD EF and EF GH, then .a.EF GHc.CD GHb.EF EFd.CD EF71. Multiplication Property of EqualityIf 4x 2 4, then .a. 4 4x 2b. 4 4x 2c.d.4x 84x 2 872. Substitution Property of EqualityIf y 3 and 8x y 12, then .a. 8(3) y 12b. 3 y 12c.d.8x 3 128x 3 1273. BD bisects ABC. m ABC 7x. m ABD 3x 25. Find m DBC.a. 50b. 125c. 75d.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.16175
Name:ID: A76. Write the conditional statement illustrated by this Venn diagram.a.b.c.d.IfIfIfIfanananananimal is a mammal, then it is a cow.animal is a cow, then it is a mammal.animal is a mammal, then it is not a cow.animal is a cow, then it is not a mammal.77. Write the contrapositive of the conditional statement illustrated by this Venn animalis not a poodle, then it is a dog.is not a dog, then it is a poodle.is not a poodle, then it is not a dog.is not a dog, then it is not a poodle.17
Name: _ Class: _ Date: _ ID: A 1 Geometry Unit 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question.
www.ck12.orgChapter 1. Basics of Geometry, Answer Key CHAPTER 1 Basics of Geometry, Answer Key Chapter Outline 1.1 GEOMETRY - SECOND EDITION, POINTS, LINES, AND PLANES, REVIEW AN- SWERS 1.2 GEOMETRY - SECOND EDITION, SEGMENTS AND DISTANCE, REVIEW ANSWERS 1.3 GEOMETRY - SECOND EDITION, ANGLES AND MEASUREMENT, REVIEW AN- SWERS 1.4 GEOMETRY - SECOND EDITION, MIDPOINTS AND BISECTORS, REVIEW AN-
Geometry Unit 10: Circles Name_ Geometry Unit 10: Circles Ms. Talhami 2 Helpful Vocabulary Word Definition/Explanation Examples/Helpful Tips Geometry Unit 10: Circles Ms. Talhami 3 Equation of a Circle Determine the center an
course. Instead, we will develop hyperbolic geometry in a way that emphasises the similar-ities and (more interestingly!) the many differences with Euclidean geometry (that is, the 'real-world' geometry that we are all familiar with). §1.2 Euclidean geometry Euclidean geometry is the study of geometry in the Euclidean plane R2, or more .
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Geometry 1st Semester Review Packet: Completed review packets are worth 20 points extra credit (on 3rd quarter homework grade) and are due the day of the exam. No late review packets will be accepted for any reason. Note: Extra credit is only available for regular Geometry and concepts Geometry.
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