Geometry Chapters 1 & 2 Test

Transcription

1 Class: Date: Geometry Chapters 1 & 2 Test 1. How many cubes would you use to make the structure below? A. 15 cubes B. 16 cubes C. 17 cubes D. 18 cubes 2. What are the names of three planes that contain point A? A. planes ABDC, ABFE, and ACHF B. planes ABDC, ABFE, and CDHG C. planes CDHG, ABFE, and ACHF D. planes ABDC, EFGH, and ACHF 3. Name the intersection of plane ACG and plane BCG. A. AC C. CG B. BG D. The planes need not intersect. 4. 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 = 45 B. x = 3, EF = 6, FG = 6 D. x = 3, EF = 8, FG = 15 1

2 5. If EG = 25, and point F is 2/5 of the way between E and G, find the value FG. The drawing is not to scale. A C. 15 B. 10 D If T is the midpoint of SU, what are ST, TU, and SU? A. ST = 7, TU = 63, and SU = 126 C. ST = 18, TU = 18, and SU = 36 B. ST = 80, TU = 80, and SU = 160 D. ST = 63, TU = 63, and SU = Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by 39 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path? A. 120 ft B. 156 ft C. 168 ft D. 84 ft 8. What conjecture can you make about the sum of the first 10 odd numbers? A. The sum is 9 10 = 90. C. The sum is = 110. B. The sum is = 100. D. The sum is = 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 = 7, then 7x 2 = 47. Statement 2: x = 7 A. x = 7 C. 7x 2 = 47 B. If 7x 2 = 47, then x = 7. D. not possible 10. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If it is Friday night, then there is a football game. If there is a football game, then Josef is wearing his school colors. It is Friday night. A. If it is Friday night, then Josef is wearing his school colors. B. Josef is wearing his school colors. C. There is a football game. D. If it is not Friday night, then Josef is not wearing his school colors. 11. 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 2000 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 2150 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. 2

3 12. BD bisects ABC. m ABC = 7x. m ABD = 3x Find m DBC. A. 108 B. 72 C. 180 D Find the values of x and y. A. x = 15, y = 17 C. x = 68, y = 112 B. x = 112, y = 68 D. x = 17, y = Plane ABC and plane BCE be the same plane. A. must B. may C. cannot 15. In the figure shown, m AED = 121. Which of the following statements is false? Not drawn to scale A. m AEB = 59 B. BEC and AED are vertical angles. C. AEB and BEC are vertical angles. D. m BEC = 121 3

4 16. Each unit on the map represents 5 miles. If you drive 20% of the way from Landview to Seaside, how many miles have you driven, and in which quadrant would you be on the map? A. 6 miles, quadrant II C. 1.2 miles, quadrant III B. 10 miles, quadrant II D. 6 miles, quadrant III 17. What are the names of four coplanar points? A. Points P, M, F, and C are coplanar. B. Points F, D, P, and N are coplanar. C. Points P, M, N, and C are coplanar. D. Points P, M, D, and C are coplanar. 18. Are points C, G, and H collinear or noncollinear? A. noncollinear B. collinear C. impossible to tell 4

5 19. Name a fourth point in plane W X V. A. X B. Z C. U D. T 20. If Z is the midpoint of RT, what are x, RZ, and RT? A. x = 18, RZ = 134, and RT = 268 C. x = 20, RZ = 150, and RT = 300 B. x = 22, RZ = 150, and RT = 300 D. x = 20, RZ = 300, and RT = Complete the statement. GDF? A. DGF C. EDF B. DEF D. DFE 5

6 22. Name an angle adjacent to DGE. A. FGI B. EGH C. HGJ D. JGI 23. What can you conclude from the information in the diagram? A. 1. LM NM 2. NQP is a right angle 3. NPQ and OPQ are vertical angles B. 1. LM LN 2. PN PO 3. PNO and LNM are adjacent angles C. 1. LM NM 2. PN PO 3. PNO and LNM are vertical angles D. 1. LM LN 2. NQP is a right angle 3. NPQ and OPQ are adjacent angles 6

7 24. MO bisects LMN, m LMN = 5x 22, m LMO = x Find m NMO. The diagram is not to scale. A B. 64 C. 59 D M(7, 5) is the midpoint of RS. The coordinates of S are (8, 7). What are the coordinates of R? A. (9, 9) B. (6, 3) C. (14, 10) D. (7.5, 6) 26. A high school soccer team is going to Columbus, Ohio to see a professional soccer game. A coordinate grid is superimposed on a highway map of Ohio. The high school is at point (3, 4) and the stadium in Columbus is at point (7, 1). The map shows a highway rest stop halfway between the cities. What are the coordinates of the rest stop? What is the approximate distance between the high school and the stadium? (One unit 8.6 miles.) 3 A. 2, 5 2, 21.5 miles C. 5, 5, 43 miles 2 3 B. 2, 5 2, 215 miles D. 5, 5 2, 5 miles 27. Ken is adding a ribbon border to the edge of his kite. Two sides of the kite measure 9.5 inches, while the other two sides measure 17.8 inches. How much ribbon does Ken need? A in. B in. C in. D in. 28. Find the area of the circle in terms of π. A. 42π in. 2 B. 1764π in. 2 C. 441π in. 2 D. 84π in. 2 7

8 29. What conjecture can you make about the sum of the first 40 positive even numbers? 2 = 2 = = 6 = = 12 = = 20 = = 30 = 5 6 A. The sum is C. The sum is B. The sum is D. The sum is 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. False B. If an angle is not a right angle, then its measure is not 90. True C. If an angle has a measure of 90, then it is a right angle. False D. If an angle has a measure of 90, then it is a right angle. True 31. A conditional can have a of true or false. A. hypothesis C. counterexample B. truth value D. conclusion 32. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 7, then x 2 = 49. A. If x 2 = 49, then x = 7. True; x 2 = 49 if and only if x = 7. B. If x 2 = 49, then x = 7. True; x = 7 if and only if x 2 = 49. C. If x 2 = 49, then x = 7. False D. If x 2 = 7, then x = 49. False 33. 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 Use the given property to complete the statement. 34. Multiplication Property of Equality If 5x 9 = 36, then. A. 5x = 324 C. 36 = 5x 9 B. 5x 9 = 324 D. 36 = 5x 9 8

9 35. What is the value of x? A. 16 B. 120 C. 60 D. 16 9

10 Geometry Chapters 1 & 2 Test Answer Section 1. ANS: C PTS: 1 DIF: L4 REF: 1-1 Nets and Drawings for Visualizing Geometry OBJ: To make nets and drawings of three-dimensional figures NAT: CC G.CO.1 G.1.d G.1.e G.3.b STA: 4.1.PO 2 TOP: 1-1 Problem 3 Isometric Drawing KEY: isometric drawing 2. ANS: A PTS: 1 DIF: L4 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 1 Naming Points, Lines, and Planes KEY: plane point 3. ANS: C PTS: 1 DIF: L4 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 3 Finding the Intersection of Two Planes KEY: plane intersection 4. ANS: A PTS: 1 DIF: L4 REF: 1-3 Measuring Segments OBJ: To find and compare lengths of segments NAT: CC G.CO.1 CC G.GPE.6 G.3.b STA: 5.2.PO 4 TOP: 1-3 Problem 2 Using the Segment Addition Postulate KEY: coordinate distance 5. ANS: C PTS: 1 DIF: L4 REF: 1-3 Measuring Segments OBJ: To find and compare lengths of segments NAT: CC G.CO.1 CC G.GPE.6 G.3.b STA: 5.2.PO 4 TOP: 1-3 Problem 2 Using the Segment Addition Postulate KEY: coordinate distance partition segment in a given ratio 6. ANS: D PTS: 1 DIF: L4 REF: 1-3 Measuring Segments OBJ: To find and compare lengths of segments NAT: CC G.CO.1 CC G.GPE.6 G.3.b STA: 5.2.PO 4 TOP: 1-3 Problem 4 Using the Midpoint KEY: midpoint 7. ANS: C PTS: 1 DIF: L4 REF: 1-8 Perimeter, Circumference, and Area OBJ: To find the perimeter or circumference of basic shapes NAT: CC N.Q.1 M.1.c M.1.f M.2.a G.3.b A.4.e STA: 5.1.PO PO 4 TOP: 1-8 Problem 1 Finding the Perimeter of a Rectangle KEY: perimeter word problem problem solving 8. ANS: B PTS: 1 DIF: L4 REF: 2-1 Patterns and Inductive Reasoning OBJ: To use inductive reasoning to make conjectures NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a STA: 4.1.PO PO PO PO PO 6 TOP: 2-1 Problem 3 Collecting Information to Make a Conjecture KEY: inductive reasoning conjecture pattern 9. ANS: C PTS: 1 DIF: L4 REF: 2-4 Deductive Reasoning OBJ: To use the Law of Detachment and the Law of Syllogism NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 STA: 4.1.PO PO PO PO PO 6 TOP: 2-4 Problem 1 Using the Law of Detachment KEY: Law of Detachment deductive reasoning 1

11 10. ANS: B PTS: 1 DIF: L4 REF: 2-4 Deductive Reasoning OBJ: To use the Law of Detachment and the Law of Syllogism NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 STA: 4.1.PO PO PO PO PO 6 TOP: 2-4 Problem 3 Using the Laws of Syllogism and Detachment KEY: deductive reasoning Law of Detachment Law of Syllogism 11. ANS: A PTS: 1 DIF: L4 REF: 2-4 Deductive Reasoning OBJ: To use the Law of Detachment and the Law of Syllogism NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 STA: 4.1.PO PO PO PO PO 6 TOP: 2-4 Problem 3 Using the Laws of Syllogism and Detachment KEY: deductive reasoning Law of Detachment Law of Syllogism 12. ANS: D PTS: 1 DIF: L4 REF: 2-5 Reasoning in Algebra and Geometry OBJ: To connect reasoning in algebra and geometry NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.b STA: 5.2.PO PO PO PO 12 TOP: 2-5 Problem 1 Justifying Steps When Solving an Equation KEY: Properties of Congruence Properties of Equality deductive reasoning 13. ANS: A PTS: 1 DIF: L4 REF: 2-6 Proving Angles Congruent OBJ: To prove and apply theorems about angles NAT: CC G.CO.9 G.5.b STA: 4.1.PO PO PO PO 12 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: Vertical Angles Theorem vertical angles supplementary angles multi-part question 14. ANS: B PTS: 1 DIF: L4 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 4 Using Postulate 1-4 KEY: reasoning plane 15. ANS: C PTS: 1 DIF: L4 REF: 1-5 Exploring Angle Pairs OBJ: To identify special angle pairs and use their relationships to find angle measures NAT: CC G.CO.1 M.1.d G.3.b STA: 5.2.PO 4 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: adjacent angles supplementary angles vertical angles 16. ANS: D PTS: 1 DIF: L4 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: To find the distance between two points in the coordinate plane NAT: CC G.GPE.6 CC G.GPE.4 CC G.GPE.7 G.3.b G.4.a STA: 4.3.PO PO PO PO 4 TOP: 1-7 Problem 4 Finding Distance KEY: coordinate plane Distance Formula problem solving partitions segment in a given ratio 17. ANS: C PTS: 1 DIF: L3 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 1 Naming Points, Lines, and Planes KEY: coplanar point 18. ANS: A PTS: 1 DIF: L3 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 1 Naming Points, Lines, and Planes KEY: point collinear points 2

12 19. ANS: C PTS: 1 DIF: L3 REF: 1-2 Points, Lines, and Planes OBJ: To understand basic terms and postulates of geometry NAT: CC G.CO.1 G.3.b G.4.b STA: 4.1.PO PO 13 TOP: 1-2 Problem 4 Using Postulate 1-4 KEY: point plane 20. ANS: C PTS: 1 DIF: L3 REF: 1-3 Measuring Segments OBJ: To find and compare lengths of segments NAT: CC G.CO.1 CC G.GPE.6 G.3.b STA: 5.2.PO 4 TOP: 1-3 Problem 4 Using the Midpoint KEY: midpoint 21. ANS: C PTS: 1 DIF: L3 REF: 1-4 Measuring Angles OBJ: To find and compare the measures of angles NAT: CC G.CO.1 M.1.d G.3.b STA: 5.2.PO 4 TOP: 1-4 Problem 3 Using Congruent Angles KEY: congruent angles 22. ANS: B PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: To identify special angle pairs and use their relationships to find angle measures NAT: CC G.CO.1 M.1.d G.3.b STA: 5.2.PO 4 TOP: 1-5 Problem 1 Identifying Angle Pairs KEY: adjacent angles 23. ANS: C PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: To identify special angle pairs and use their relationships to find angle measures NAT: CC G.CO.1 M.1.d G.3.b STA: 5.2.PO 4 TOP: 1-5 Problem 2 Making Conclusions From a Diagram KEY: vertical angles supplementary angles adjacent angles right angle congruent segments 24. ANS: C PTS: 1 DIF: L3 REF: 1-5 Exploring Angle Pairs OBJ: To identify special angle pairs and use their relationships to find angle measures NAT: CC G.CO.1 M.1.d G.3.b STA: 5.2.PO 4 TOP: 1-5 Problem 4 Using an Angle Bisector to Find Angle Measures KEY: angle bisector 25. ANS: B PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: To find the midpoint of a segment NAT: CC G.GPE.6 CC G.GPE.4 CC G.GPE.7 G.3.b G.4.a STA: 4.3.PO PO PO PO 4 TOP: 1-7 Problem 2 Finding an Endpoint KEY: coordinate plane Midpoint Formula 26. ANS: C PTS: 1 DIF: L3 REF: 1-7 Midpoint and Distance in the Coordinate Plane OBJ: To find the distance between two points in the coordinate plane NAT: CC G.GPE.6 CC G.GPE.4 CC G.GPE.7 G.3.b G.4.a STA: 4.3.PO PO PO PO 4 KEY: Distance Formula coordinate plane word problem problem solving midpoint 27. ANS: C PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: To find the perimeter or circumference of basic shapes NAT: CC N.Q.1 M.1.c M.1.f M.2.a G.3.b A.4.e STA: 5.1.PO PO 4 TOP: 1-8 Problem 1 Finding the Perimeter of a Rectangle KEY: perimeter problem solving word problem 28. ANS: C PTS: 1 DIF: L3 REF: 1-8 Perimeter, Circumference, and Area OBJ: To find the area of basic shapes TOP: 1-7 Problem 4 Finding Distance NAT: CC N.Q.1 M.1.c M.1.f M.2.a G.3.b A.4.e STA: 5.1.PO PO 4 TOP: 1-8 Problem 5 Finding Area of a Circle KEY: area circle 3

13 29. ANS: C PTS: 1 DIF: L3 REF: 2-1 Patterns and Inductive Reasoning OBJ: To use inductive reasoning to make conjectures NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a STA: 4.1.PO PO PO PO PO 6 TOP: 2-1 Problem 3 Collecting Information to Make a Conjecture KEY: inductive reasoning pattern conjecture 30. ANS: D PTS: 1 DIF: L2 REF: 2-2 Conditional Statements OBJ: To write converses, inverses, and contrapositives of conditionals NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 TOP: 2-2 Problem 4 Writing and Finding Truth Values of Statements KEY: conditional statement converse of a conditional truth value 31. ANS: B PTS: 1 DIF: L3 REF: 2-2 Conditional Statements OBJ: To recognize conditional statements and their parts NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.a STA: 4.1.PO PO PO PO PO 6 TOP: 2-2 Problem 3 Finding the Truth Value of a Conditional KEY: conditional statement truth value 32. ANS: C PTS: 1 DIF: L3 REF: 2-3 Biconditionals and Definitions OBJ: To write biconditionals and recognize good definitions NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.1.c STA: 5.2.PO PO PO PO 13 TOP: 2-3 Problem 1 Writing a Biconditional KEY: conditional statement converse of a conditional biconditional statement 33. ANS: D PTS: 1 DIF: L3 REF: 2-4 Deductive Reasoning OBJ: To use the Law of Detachment and the Law of Syllogism NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 STA: 4.1.PO PO PO PO PO 6 TOP: 2-4 Problem 1 Using the Law of Detachment KEY: deductive reasoning Law of Detachment 34. ANS: A PTS: 1 DIF: L3 REF: 2-5 Reasoning in Algebra and Geometry OBJ: To connect reasoning in algebra and geometry NAT: CC G.CO.9 CC G.CO.10 CC G.CO.11 G.5.b STA: 5.2.PO PO PO PO 12 TOP: 2-5 Problem 2 Using Properties of Equality and Congruence KEY: Properties of Equality 35. ANS: D PTS: 1 DIF: L3 REF: 2-6 Proving Angles Congruent OBJ: To prove and apply theorems about angles NAT: CC G.CO.9 G.5.b STA: 4.1.PO PO PO PO 12 TOP: 2-6 Problem 1 Using the Vertical Angles Theorem KEY: vertical angles Vertical Angles Theorem 4

14 Geometry Chapters 1 2 Test [Answer Strip] _ C 5. _ D 12. _ D 16. _ C 19. _ C 1. _ A 13. _ D 6. _ C 20. _ A 2. _ C 7. _ C 17. _ B 8. _ B 14. _ C 21. _ C 9. _ C 15. _ B 10. _ C 3. _ A 4. _ A 11. _ A 18.

15 Geometry Chapters 1 2 Test [Answer Strip] _ B 22. _ C 24. _ C 29. _ D 35. _ D 30. _ B 25. _ C 26. _ C 23. _ B 31. _ C 32. _ C 27. _ C 28. _ D 33. _ A 34.