Cocoa and Cram Midterm Review for Geometry

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1 Name: Cocoa and Cram Midterm Review for Geometry 1. PR is represented by which sketch? a. c. b. d. 2. Two distinct planes intersect. Describe their intersection. Draw a sketch to support your answer. 3. Sketch the intersection of a line and a plane. 4. The notation for the length of the segment between P and Q is. a. PQ b. PQ c. QP d. PQ 5. Let C be between D and E. Use the Segment Addition Postulate to solve for v. DC = 3v 30 CE = 6v 15 DE = 27 a. v = 3 b. v = 11 c. v = 5 d. v = 8 1

2 AB = x + 16, BC = 5x + 10, AC = Find AB and BC in the situation shown above. 7. Find the distance between the points (1, 4) and ( 2, 1). a. 10 c. 34 b. 10 d The distance between points A and B is. a. 13 b. 11 c. 85 d Find the midpoint of the segment with endpoints (9, 8) and (3, 5). a. (3, 3 ) 2 c. 13 (6, 2 ) b. (12, 13) d. (1, 2) 10. Find the distance between the points (1, 8) and ( 7, 2). 2

3 11. The midpoint of JK is MÊ Ë Á 2, 2ˆ. One endpoint is J(4, 3). Find the coordinates of the other endpoint. 12. Find the circumference of the circle. Use π = a in. b in. c in. d in. 13. Find the area and circumference of the circle. Use π = A can of paint will cover 108 square feet. How many cans of paint are needed to paint a wall 6 feet high and 75 feet long? 3

4 15. Refer to the figure. Which theorem guarantees l and m are parallel? a. Alternate Interior Angles Converse b. Consecutive Interior Angles Converse c. Corresponding Angles Converse d. Alternate Exterior Angles Converse 16. Tell whether lines m and n are parallel or not parallel and explain. 17. Find the slope of the line passing through the points A(6, 5) and B( 5, 7). a b c Which best describes the relationship between Line 1 and Line 2? Line 1 passes through Ê Ë 3, 6 Ê Ë Á 7, 11 ˆ Line 2 passes through Ê Ë 1, 8 Ê Ë Á 4, 4 ˆ a. perpendicular b. They are the same line. c. parallel d. neither perpendicular nor parallel 19. Find the slope of a line perpendicular to the line containing the points (3, 7) and (4, 3). d A segment with endpoints on a circle is a. a. secant c. tangent b. radius d. chord 4

5 21. A line which intersects a circle at exactly one point is called. a. a point of tangency c. a chord b. a tangent line d. a secant 22. You are standing at point B. Point B is 16 feet from the center of the circular water storage tank and 15 feet from point A. AB is tangent to ño at A. Find the radius of the tank. a ft. c ft. b ft. d. 5.6 ft. Use the diagram (not drawn to scale) and the given information to find the diameter of the circle. Round your answer to the nearest tenth. 23. BC=18 and DC=22. a c. 7.3 b. 8.9 d

6 Find the value of x. 24. a. 4 c. 24 b. 8 d a. 3 c. none of these b. 5 d Write the standard equation of a circle with its center at the origin and radius 3. a. x 2 + y 2 = 6 c. x 2 + y 2 = 9 b. x y 2 6 = 1 d. x 2 + y 2 = Write the standard equation of a circle with center ( 3, 4) and radius 6. a. ( x 3) 2 Ê Ë Á y 4ˆ 2 = 6 c. ( x+ 3) 2 + Ê Ë Á y 4ˆ 2 = 36 b. ( x 3) 2 + Ê Ë Á y 4ˆ 2 = 6 d. ( x+ 3) 2 + Ê Ë Á y+ 4ˆ 2 = 36 6

7 28. A small messenger company can deliver only in a small part of the city. Write an equation for the boundary where the company delivers, and find its radius. Each unit represents one block. a. ( x+ 2) 2 + Ê Ë Á y+ 5ˆ 2 = 50; r = 25 blocks b. ( x+ 2) 2 + Ê Ë Á y+ 5ˆ 2 = 50; r = 5 blocks c. ( x 5) 2 + Ê Ë Á y 2ˆ 2 = 25; r = 25 blocks d. ( x 5) 2 + Ê Ë Á y 2ˆ 2 = 25; r = 5 blocks Use the diagram (not draw to scale) and the given information. 29. Find the value of x if mab= 20 and mcd= 62. a. 41 c. 21 b. 43 d Find the value of x if mab = 59 and mcd = 47. 7

8 31. A hummingbird is flying toward a large tree that has a radius of 6 feet. When it is 31 feet from the center of the tree, its lines of sight form two tangents. What is the measure of the arc on the tree that the hummingbird can see? a c b d Find the measure of Find the value of x. a c. 6.7 b d

9 34. Given AC bisects BD, choose the true statement that refers to the figure. a. CD = BA c. AC is a diameter. b. BCD is a major arc. d. BAD is a minor arc. 35. Given circle O with radius 5 and OC = 3. Find the length of AB. 36. The area of a regular octagon is 25 cm 2. What is the area of a regular octagon with sides five times as large as the sides of the first octagon? a. 690 cm 2 c. 125 cm 2 b cm 2 d. 625 cm The ratio of the side lengths of two regular hexagons is 4 to 9. If the area of the smaller hexagon is 16 square units, then the area of the larger hexagon is. a. 81 sq. units c. 36 sq. units 256 b. 81 sq. units d. 64 sq. units Maria needs to make a poster that is 2.5 m by 3 m for the big game. The cost of the paper is $2.50. Later she needs another poster with dimensions 1.25 m by 1.5 m. What is the paper for this poster likely to cost? a. $0.88 c. $1.25 b. $0.63 d. $1.00 9

10 ID: A Cocoa and Cram Midterm Review for Geometry Answer Section 1. ANS: C PTS: 1 DIF: Level A REF: MHGT0077 TOP: Lesson 1.1 Identify Points, Lines, and Planes KEY: identify ray 2. ANS: They intersect in a line. PTS: 1 DIF: Level B REF: MLGE0220 TOP: Lesson 1.1 Identify Points, Lines, and Planes 3. ANS: Sketches vary. KEY: plane intersects draw PTS: 1 DIF: Level A REF: MLGE0184 TOP: Lesson 1.1 Identify Points, Lines, and Planes KEY: draw plane intersects line 4. ANS: D PTS: 1 DIF: Level A REF: MHGT0075 TOP: Lesson 1.2 Use Segments and Congruence KEY: notation segment length 5. ANS: D PTS: 1 DIF: Level B REF: MHGM0013 TOP: Lesson 1.2 Use Segments and Congruence KEY: solve variable segment addition postulate BLM: Application 1

11 ID: A 6. ANS: AB = 21, BC = 35 PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.REP.2 NCTM 9-12.PRS.3 STA: NY.NYLES.MTH.05.GEO.G.PS.1 NY.NYLES.MTH.05.GEO.G.PS.5 NY.NYLES.MTH.05.GEO.G.CM.2 NY.NYLES.MTH.05.GEO.G.G.67 TOP: Lesson 1.2 Use Segments and Congruence KEY: equation length segment 7. ANS: D PTS: 1 DIF: Level A REF: DBTM0807 NAT: NCTM 9-12.GEO.2.a STA: NY.NYLES.MTH.05.GEO.G.G.67 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: distance formula coordinate geometry BLM: Application 8. ANS: C PTS: 1 DIF: Level B REF: MLGE0188 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: distance formula coordinate geometry BLM: Application 9. ANS: C PTS: 1 DIF: Level A REF: AKA20905 NAT: NCTM 9-12.GEO.2.a STA: NY.NYLES.MTH.05.GEO.G.G.66 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: midpoint formula 10. ANS: 10 units PTS: 1 DIF: Level A REF: PAIA0304 NAT: NCTM 9-12.GEO.2.a STA: NY.NYLES.MTH.05.GEO.G.G.67 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: distance formula coordinate geometry BLM: Application 11. ANS: ( 8, 7) PTS: 1 DIF: Level B REF: MLGE0086 NAT: NCTM 9-12.GEO.2.a STA: NY.NYLES.MTH.05.GEO.G.G.66 TOP: Lesson 1.3 Use Midpoint and Distance Formulas KEY: midpoint formula BLM: Synthesis 12. ANS: D PTS: 1 DIF: Level B REF: MLGE0395 TOP: Lesson 1.7 Find Perimeter, Circumference, and Area KEY: circle circumference 13. ANS: Area: square units, Circumference: units PTS: 1 DIF: Level B REF: MLGE0394 NAT: NCTM 9-12.MEA.2.b TOP: Lesson 1.7 Find Perimeter, Circumference, and Area KEY: circle area circumference 2

12 ID: A 14. ANS: 5 PTS: 1 DIF: Level B REF: HLGM0077 NAT: NCTM 9-12.MEA.2.b NCTM 9-12.PRS.2 TOP: Lesson 1.7 Find Perimeter, Circumference, and Area KEY: area rectangle 15. ANS: D PTS: 1 DIF: Level A REF: MGEH0029 TOP: Lesson 3.3 Prove Lines are Parallel KEY: converse Alternate Exterior Angles BLM: Comprehension 16. ANS: parallel; Corresponding Angles Converse PTS: 1 DIF: Level B REF: BS NAT: NCTM 9-12.PRS.4 NCTM 9-12.REA.1 NCTM 9-12.COM.3 STA: NY.NYLES.MTH.05.GEO.G.RP.2 NY.NYLES.MTH.05.GEO.G.CM.5 NY.NYLES.MTH.05.GEO.G.G.57 TOP: Lesson 3.3 Prove Lines are Parallel KEY: line angle parallel TAAS3 corresponding TEKSe2A BLM: Analysis 17. ANS: D PTS: 1 DIF: Level A REF: DBIM0706 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: slope 18. ANS: A PTS: 1 DIF: Level B REF: MHGM0007 STA: NY.NYLES.MTH.05.GEO.G.RP.2 NY.NYLES.MTH.05.GEO.G.G.63 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: line slope parallel perpendicular 19. ANS: 1 4 PTS: 1 DIF: Level B REF: PEBA0612 TOP: Lesson 3.4 Find and Use Slopes of Lines KEY: line slope parallel perpendicular point slope formula BLM: Comprehension 20. ANS: D PTS: 1 DIF: Level A REF: MLGE0166 TOP: Lesson 10.1 Use Properties of Tangents KEY: circle chord endpoint segment 21. ANS: B PTS: 1 DIF: Level A REF: HLGM0950 TOP: Lesson 10.1 Use Properties of Tangents KEY: circle tangent intersect 22. ANS: D PTS: 1 DIF: Level B REF: MHGM0071 STA: NY.NYLES.MTH.05.GEO.G.G.48 NY.NYLES.MTH.05.GEO.G.G.50.a NY.NYLES.MTH.05.GEO.G.G.50.b NY.NYLES.MTH.05.GEO.G.G.53.a TOP: Lesson 10.1 Use Properties of Tangents KEY: solve circle tangent Pythagorean 3

13 ID: A 23. ANS: B PTS: 1 DIF: Level B REF: BMGM0103 STA: NY.NYLES.MTH.05.GEO.G.G.48 NY.NYLES.MTH.05.GEO.G.G.50.a NY.NYLES.MTH.05.GEO.G.G.50.b NY.NYLES.MTH.05.GEO.G.G.53.a TOP: Lesson 10.6 Find Segment Lengths in Circles KEY: circle diameter secant segment BLM: Comprehension 24. ANS: A PTS: 1 DIF: Level A REF: XMOD0509 STA: NY.NYLES.MTH.05.GEO.G.G.49.a NY.NYLES.MTH.05.GEO.G.G.51.a NY.NYLES.MTH.05.GEO.G.G.53.d TOP: Lesson 10.6 Find Segment Lengths in Circles KEY: circle chord length chords 25. ANS: B PTS: 1 DIF: Level A REF: XMOD0510 STA: NY.NYLES.MTH.05.GEO.G.G.53.c TOP: Lesson 10.6 Find Segment Lengths in Circles KEY: circle chord length 26. ANS: C PTS: 1 DIF: Level A REF: DBYM0909 STA: NY.NYLES.MTH.05.GEO.G.G.71 TOP: Lesson 10.7 Write and Graph Equations of Circles KEY: equation circle radius 27. ANS: D PTS: 1 DIF: Level A REF: DBIM0719 STA: NY.NYLES.MTH.05.GEO.G.G.71 TOP: Lesson 10.7 Write and Graph Equations of Circles KEY: equation identify circle radius center BLM: Knowledge 28. ANS: D PTS: 1 DIF: Level B REF: MLGE0251 STA: NY.NYLES.MTH.05.GEO.G.G.72 NY.NYLES.MTH.05.GEO.G.G.73 TOP: Lesson 10.7 Write and Graph Equations of Circles KEY: equation graph circle 29. ANS: A PTS: 1 DIF: Level B REF: MLGE0108 STA: NY.NYLES.MTH.05.GEO.G.G.51.a TOP: Lesson 10.5 Apply Other Angle Relationships in Circles KEY: circle chord angle BLM: Comprehension 30. ANS: 53 PTS: 1 DIF: Level B REF: MLGE0107 STA: NY.NYLES.MTH.05.GEO.G.G.51.a TOP: Lesson 10.5 Apply Other Angle Relationships in Circles KEY: circle chord angle BLM: Comprehension 31. ANS: B PTS: 1 DIF: Level C REF: MLGE0249 NAT: NCTM 9-12.PRS.2 STA: NY.NYLES.MTH.05.GEO.G.G.50.a NY.NYLES.MTH.05.GEO.G.G.50.b NY.NYLES.MTH.05.GEO.G.G.53.a TOP: Lesson 10.5 Apply Other Angle Relationships in Circles KEY: word trigonometric inverse BLM: Synthesis 4

14 ID: A 32. ANS: 56 PTS: 1 DIF: Level A REF: HLGM1005 STA: NY.NYLES.MTH.05.GEO.G.G.51.c TOP: Lesson 10.5 Apply Other Angle Relationships in Circles KEY: angle measure 33. ANS: C PTS: 1 DIF: Level B REF: PHGM1209 STA: NY.NYLES.MTH.05.GEO.G.G.48 TOP: Lesson 10.3 Apply Properties of Chords KEY: circle radius chord BLM: Analysis 34. ANS: C PTS: 1 DIF: Level A REF: HLGM0980 STA: NY.NYLES.MTH.05.GEO.G.G.49.a TOP: Lesson 10.3 Apply Properties of Chords KEY: diameter 35. ANS: 8 PTS: 1 DIF: Level B REF: MGEO0023 STA: NY.NYLES.MTH.05.GEO.G.G.48 NY.NYLES.MTH.05.GEO.G.G.50.a NY.NYLES.MTH.05.GEO.G.G.50.b NY.NYLES.MTH.05.GEO.G.G.53.a TOP: Lesson 10.3 Apply Properties of Chords KEY: circle chord Pythagorean 36. ANS: D PTS: 1 DIF: Level B REF: MLGE0428 TOP: Lesson 11.3 Perimeter and Area of Similar Figures KEY: area polygon ratio of similarity 37. ANS: A PTS: 1 DIF: Level A REF: MLGE0264 NAT: NCTM 9-12.GEO.1.b TOP: Lesson 11.3 Perimeter and Area of Similar Figures KEY: ratio area similar hexagon 38. ANS: B PTS: 1 DIF: Level B REF: MHGM0104 NAT: NCTM 9-12.MEA.2.b NCTM 9-12.PRS.2 TOP: Lesson 11.3 Perimeter and Area of Similar Figures KEY: word proportion 5

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC? 0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle