Geometry Final 2012 Review

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

____ 1. The length of is shown. What other length can you determine for this diagram?

F

DG

E

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|12

a. EF = 12 c. DF = 24b. DG = 12 d. No other length can be determined.

____ 2. Which statement can you conclude is true from the given information?

Given: is the perpendicular bisector of

I K

B

A

J

a. AJ = BJ c. IJ = JKb. is a right angle. d. A is the midpoint of .

____ 3. Which statement is not necessarily true?

Given: is the bisector of

J L

E

D

K

a. DK = KE c. K is the midpoint of .

b. d. DJ = DL____ 4. Where can the perpendicular bisectors of the sides of a right triangle intersect?

I. inside the triangleII. on the triangleIII. outside the trianglea. I only b. II only c. I or II only d. I, II, or II

____ 5. Where can the bisectors of the angles of an obtuse triangle intersect?I. inside the triangleII. on the triangleIII. outside the trianglea. I only b. III only c. I or III only d. I, II, or II

____ 6. Where can the medians of a triangle intersect?I. inside the triangleII. on the triangleIII. outside the trianglea. I only b. III only c. I or III only d. I, II, or II

____ 7. Where can the lines containing the altitudes of an obtuse triangle intersect?I. inside the triangleII. on the triangleIII. outside the trianglea. I only b. I or II only c. III only d. I, II, or II

____ 8. Which diagram shows a point P an equal distance from points A, B, and C?a. c.

b. d.

____ 9. Name the smallest angle of The diagram is not to scale.

A B

C

5 6

7

a.b.c. Two angles are the same size and smaller than the third.d.

____ 10. Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 158 ft from camera 2, which was 121 ft from Camera 3. Cameras 1 and 3 were 140 ft apart. Which camera had to cover the greatest angle?a. camera 2 b. camera 1 c. cannot tell d. camera 3

____ 11. Jay, Kay, and Ray found themselves far apart when they stopped for lunch while working in a field. Jay could see Kay, then turn through 75° and see Ray. Kay could see Ray, then turn through 50° and see Jay. Ray could see Jay, then turn through 55° and see Kay. Which two were farthest apart?a. Kay and Rayb. Jay and Kayc. Ray and Jayd. Kay and Ray were the same distance apart as Ray and Jay.

____ 12. Which three lengths could be the lengths of the sides of a triangle?a. 12 cm, 5 cm, 17 cm c. 9 cm, 22 cm, 11 cmb. 10 cm, 15 cm, 24 cm d. 21 cm, 7 cm, 6 cm

____ 13. Which three lengths can NOT be the lengths of the sides of a triangle?a. 23 m, 17 m, 14 m c. 5 m, 7 m, 8 mb. 11 m, 11 m, 12 m d. 21 m, 6 m, 10 m

____ 14. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side?a. c. x > 10 and x < 18b. x > 8 and x < 28 d.

____ 15. Two sides of a triangle have lengths 6 and 17. Which expression describes the length of the third side?a. at least 11 and less than 23 c. greater than 11 and at most 23b. at least 11 and at most 23 d. greater than 11 and less than 23

____ 16. Judging by appearance, classify the figure in as many ways as possible.

�

�

�

�

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|

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a. rectangle, square, quadrilateral, parallelogram, rhombusb. rectangle, square, parallelogramc. rhombus, trapezoid, quadrilateral, squared. square, rectangle, quadrilateral

____ 17. Which statement is true?a. All quadrilaterals are rectangles.b. All quadrilaterals are squares.c. All rectangles are quadrilaterals.d. All quadrilaterals are parallelograms.

____ 18. Judging by appearances, which figure is a trapezoid?a. c.

b. d.

____ 19. WXYZ is a parallelogram. Name an angle congruent to

X

ZW

Y

N

a. b. c. d.

____ 20. What is the missing reason in the proof?Given: parallelogram ABCD with diagonal Prove:

D

BA

C

Statements Reasons

1. 1. Definition of parallelogram

2. 2. Alternate Interior Angles Theorem

3. 3. Definition of parallelogram

4. 4. Alternate Interior Angles Theorem

5. 5. Reflexive Property of Congruence

6. 6. ?

a. Reflexive Property of Congruence c. Alternate Interior Angles Theoremb. ASA d. SSS

____ 21. Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?X

ZW

Y

N

a. c.b. d.

____ 22. Lucinda wants to build a square sandbox, but has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length.a. Arrange four equal-length sides so the diagonals bisect each other.b. Arrange four equal-length sides so the diagonals are equal lengths also.c. Make each diagonal the same length as four equal-length sides.d. Not possible; Lucinda has to be able to measure a right angle.

____ 23. Which description does NOT guarantee that a quadrilateral is a parallelogram?a. a quadrilateral with both pairs of opposite sides congruentb. a quadrilateral with the diagonals bisecting each otherc. a quadrilateral with consecutive angles supplementary

d. quadrilateral with two opposite sides parallel____ 24. Which diagram shows the most useful positioning of a square in the first quadrant of a coordinate plane?

a. c.

b. d.

____ 25. Which diagram shows the most useful positioning and accurate labeling of a kite in the coordinate plane?a. c.

b. d.

Short Answer

26. Identify parallel segments in the diagram.

A

C

E

DB D

F5 5

6

6

8

8

27. B is the midpoint of and D is the midpoint of Solve for x, given and

A

C

E

B D

28. Given: is the perpendicular bisector of IK. Name two lengths that are equal.

I K

B

A

J

29. In draw median FJ from F to the side opposite F.

F G

H

30. Write the inverse of this statement:If a number is divisible by two, then it is even.

31. To prove “p is equal to q” using an indirect proof, what would your starting assumption be?

32. Given points A(2, 3) and B(–2, 5), explain how you could use the Distance Formula and an indirect argument to show that point C(0, 3) is NOT the midpoint of .

33. Can these three segments form the sides of a triangle? Explain.

a

bc

34. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.

2x + 6 5y

5x

7y + 7

35. What type of quadrilateral has exactly one pair of parallel sides?

36. Isosceles trapezoid ABCD has legs and and base If AB = 4y – 3, BC = 3y – 4, and CD = 5y – 10, find the value of y.

37. One side of a kite is 6 cm less than 4 times the length of another. The perimeter of the kite is 68 cm. Find the length of each side of the kite.

38. For parallelogram PQRS, find the values of x and y. Then find PT, TR, ST, and TQ. The diagram is not to scale.

39. Complete this statement: For parallelogram ABCD, Then state a definition or theorem that justifies your answer.

D

BA

C

O

40. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.

|

1

|2

3

2

4

|

|

41. Draw two noncongruent kites A and B such that the sides of kite A are congruent to the sides of kite B.

42. Judging by appearance, classify the figure in as many ways as possible using rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus.

Draw a net for the figure shown. Label the net with its dimensions.

43.

44.

Consider the prism shown below.a. Draw a net for the prism and label all dimensions.b. Use the net to find the surface area of the prism.

45.

46.

Essay

47. Write a two column proof.

Given: Prove:

F B

D

A

E C

48. AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.

D

C

A

BE

5

12

13

49. Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle.

50. A 16-foot ladder is placed against the side of a building as shown in Figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, the ladder is moved 4 feet closer to the base of the building as shown in Figure 2.

To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer.

51. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim? Show your work.

52. Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter.

53. Erica made a cylindrical pottery vase with a height of 45 cm and a diameter of 14 cm.a. Erica wants to paint just the sides of the vase. To the nearest whole number, find the

number of square centimeters she will need to paint. Explain the method you use to find the lateral area.

b. Erica’s friend Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you use to find the radius.

54. A log cabin is shaped like a rectangular prism. A model of the cabin has a scale of 1 centimeter to 0.5 meters.a. If the model is 14 cm by 20 cm by 7 cm, what are the dimensions of the actual log

cabin? Explain how you find the dimensions.b. What is the volume of the actual log cabin? Explain how you find the volume.c. What is the ratio of the volume of the model of the cabin to the volume of the actual

cabin? Explain your method for finding the ratio.

55. A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.

Other

56. A conditional statement and its contrapositive have the same truth value and are called equivalent statements. How are the inverse and converse of a conditional statement related to each other?

57. A tennis court has a baseline at each end. One is labeled in the picture. Which part of the tennis court is equidistant from the midpoints of the two baselines? Explain.

58. ABCD is a rhombus. Explain why .

A

CD

B

59. Is the quadrilateral a parallelogram? Explain. The diagram is not to scale.

41°

139°

139°

A B

C D

60. All of the angles of a quadrilateral are congruent. Can the quadrilateral be a parallelogram? Explain.

61. Can this quadrilateral be a parallelogram? Explain.

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||

62. A triangle has sides that measure 33 cm, 65 cm, and 56 cm. Is it a right triangle? Explain.

63. Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.

a. What is the volume of the cylinder? Explain your method for finding the volume.b. What is the total volume of the three balls? Explain your method for finding the total

volume.c. What percent of the volume of the container is occupied by the three balls? Explain

how you find the percent.

64. Katie approximated the volume and the surface area for a ball she was using for some exercises by assuming the ball is a sphere. She was surprised when the numerical value of the volume in cubic inches was the same as the numerical value of the surface area in square inches. What is the radius of the ball? Explain your method for finding the radius.

Geometry Final 2012 ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: A DIF: L1 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3TOP: 5-2 Example 1 KEY: perpendicular bisector,Perpendicular Bisector TheoremMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

2. ANS: C DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3KEY: perpendicular bisector,Perpendicular Bisector Theorem,reasoningMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

3. ANS: A DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3KEY: Perpendicular Bisector Theorem,perpendicular bisector,reasoningMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

4. ANS: B DIF: L3 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.1 Properties of Bisectors STO: NJ 4.2.A.3KEY: circumcenter of the triangle,perpendicular bisector,reasoning,right triangleMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

5. ANS: A DIF: L2 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.1 Properties of Bisectors STO: NJ 4.2.A.3KEY: incenter of the triangle,angle bisector,reasoningMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

6. ANS: A DIF: L2 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.2 Medians and Altitudes STO: NJ 4.2.A.3KEY: median of a triangle,centroid,reasoningMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

7. ANS: C DIF: L2 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.2 Medians and Altitudes STO: NJ 4.2.A.3KEY: altitude of a triangle,orthocenter of the triangleMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

8. ANS: A DIF: L1 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.1 Properties of Bisectors STO: NJ 4.2.A.3 TOP: 5-3 Example 2KEY: circumcenter of the triangle,circumscribeMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

9. ANS: D DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.1 Inequalities Involving Angles of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 2 KEY: Theorem 5-10

MSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

10. ANS: D DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.1 Inequalities Involving Angles of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 2 KEY: word problem,problem solving,Theorem 5-10MSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

11. ANS: A DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 3 KEY: problem solving,word problem,Theorem 5-11MSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

12. ANS: B DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 4 KEY: Triangle Inequality TheoremMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

13. ANS: D DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 4 KEY: Triangle Inequality TheoremMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

14. ANS: B DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 5 KEY: Triangle Inequality TheoremMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

15. ANS: D DIF: L1 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3TOP: 5-5 Example 5 KEY: Triangle Inequality TheoremMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

16. ANS: A DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3TOP: 6-1 Example 1KEY: special quadrilaterals,quadrilateral,parallelogram,rhombus,square,rectangle,kite,trapezoidMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

17. ANS: C DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3KEY: reasoning,kite,parallelogram,quadrilateral,rectangle,rhombus,special quadrilateralsMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

18. ANS: B DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3KEY: trapezoidMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

19. ANS: D DIF: L1 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles STO: NJ 4.2.A.3 KEY: parallelogram,opposite angles

MSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16

20. ANS: B DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals STO: NJ 4.2.A.3KEY: proof,two-column proof,parallelogram,diagonalMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16

21. ANS: A DIF: L2 REF: 6-3 Proving That a Quadrilateral is a ParallelogramOBJ: 6-3.1 Is the Quadrilateral a Parallelogram? STO: NJ 4.2.A.3KEY: proof,reasoning,parallelogramMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16, TV.LV20.17, TV.LV20.18

22. ANS: B DIF: L2 REF: 6-4 Special ParallelogramsOBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? STO: NJ 4.2.A.3TOP: 6-4 Example 4KEY: square,reasoning,Theorem 6-10,Theorem 6-11,word problem,problem solvingMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

23. ANS: D DIF: L2 REF: 6-4 Special ParallelogramsOBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? STO: NJ 4.2.A.3KEY: square,reasoningMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

24. ANS: C DIF: L1 REF: 6-6 Placing Figures in the Coordinate PlaneOBJ: 6-6.1 Naming Coordinates STO: NJ 4.2.C.1KEY: algebra,coordinate plane,rectangle,squareMSC: NAEP G4d, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.17, TV.LV20.52

25. ANS: D DIF: L2 REF: 6-6 Placing Figures in the Coordinate PlaneOBJ: 6-6.1 Naming Coordinates STO: NJ 4.2.C.1KEY: algebra,coordinate plane,isosceles trapezoid,kiteMSC: NAEP G4d, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.17, TV.LV20.52

SHORT ANSWER

26. ANS:

DIF: L1 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments STO: NJ 4.2.A.3TOP: 5-1 Example 2 KEY: midsegment,parallel lines,Triangle Midsegment TheoremMSC: NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

27. ANS:

DIF: L2 REF: 5-1 Midsegments of Triangles

OBJ: 5-1.1 Using Properties of Midsegments STO: NJ 4.2.A.3KEY: Triangle Midsegment Theorem,midsegmentMSC: NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

28. ANS:IJ and JK

DIF: L1 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3TOP: 5-2 Example 1 KEY: perpendicular bisector,Perpendicular Bisector TheoremMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

29. ANS:

F G

H

J

|

|

DIF: L1 REF: 5-3 Concurrent Lines¸ Medians¸ and AltitudesOBJ: 5-3.2 Medians and Altitudes STO: NJ 4.2.A.3 KEY: median of a triangleMSC: NAEP G3b, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

30. ANS:If a number is not divisible by two¸ then it is not even.

DIF: L1 REF: 5-4 Inverses¸ Contrapositives¸ and Indirect ReasoningOBJ: 5-4.1 Writing the Negation¸ Inverse¸ and Contrapositive STO: NJ 4.2.A.4TOP: 5-4 Example 2 KEY: contrapositive,conditional statement,inverseMSC: NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17

31. ANS:p is not equal to q.

DIF: L1 REF: 5-4 Inverses¸ Contrapositives¸ and Indirect ReasoningOBJ: 5-4.2 Using Indirect Reasoning STO: NJ 4.2.A.4 TOP: 5-4 Example 3KEY: indirect reasoning,indirect proofMSC: NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17

32. ANS:Assume that C(0, 3) is the midpoint of . By the Distance Formula,

AC BCwhich contradicts the assumption that C is the midpoint of .Therefore, C is not the midpoint of .

DIF: L2 REF: 5-4 Inverses¸ Contrapositives¸ and Indirect ReasoningOBJ: 5-4.2 Using Indirect Reasoning STO: NJ 4.2.A.4KEY: indirect proof,indirect reasoning,Distance Formula,proofMSC: NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17

33. ANS:No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater than the length of the third segment.

DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles STO: NJ 4.2.A.3KEY: Triangle Inequality TheoremMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

34. ANS:x = 7, y = 4; 20, 35

DIF: L2 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3TOP: 6-1 Example 3 KEY: algebra,rectangleMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

35. ANS:trapezoid

DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3KEY: quadrilateral,reasoning,algebra,trapezoid,rhombus,square,parallelogramMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

36. ANS:7

DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3KEY: isosceles trapezoid,algebraMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

37. ANS:8 cm , 26 cm

DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3KEY: kite,algebra,word problem,problem solvingMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

38. ANS:x = 3, y = 6; 5, 5, 7, 7

DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals STO: NJ 4.2.A.3TOP: 6-2 Example 3 KEY: parallelogram,algebra,multi-part questionMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16

39. ANS:OD; the diagonals of a parallelogram bisect each other.

DIF: L1 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals STO: NJ 4.2.A.3KEY: parallelogram,diagonal,Theorem 6-3MSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16

40. ANS:Rhombus; the measure of all numbered angles equal 39.

DIF: L1 REF: 6-4 Special ParallelogramsOBJ: 6-4.1 Diagonals of Rhombuses and Rectangles STO: NJ 4.2.A.3KEY: parallelogram,rhombus,reasoningMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

41. ANS:Answers may vary. Sample:

| |

|| |

| | |

|| |

|

DIF: L2 REF: 6-5 Trapezoids and KitesOBJ: 6-5.1 Properties of Trapezoids and Kites STO: NJ 4.2.A.3KEY: kiteMSC: NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

42. ANS:parallelogram, quadrilateral

DIF: L1 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals STO: NJ 4.2.A.3TOP: 6-1 Example 1KEY: quadrilateral,parallelogram,rectangle,rhombus,square,trapezoidMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

43. ANS:

Answers may vary. Sample answer:

DIF: L1 REF: 10-1 Space Figures and NetsOBJ: 10-1.1 Identifying Nets of Space Figures STO: NJ 4.2.B.2TOP: 10-1 Example 2 KEY: net,rectangular prismMSC: NAEP G1b, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14, TV.LV20.17

44. ANS:Answers may vary. Sample answer:

DIF: L1 REF: 10-1 Space Figures and NetsOBJ: 10-1.1 Identifying Nets of Space Figures STO: NJ 4.2.B.2TOP: 10-1 Example 2 KEY: net,triangular prismMSC: NAEP G1b, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.14, TV.LV20.17

45. ANS:a.

b. 184 m

DIF: L1 REF: 10-3 Surface Areas of Prisms and CylindersOBJ: 10-3.1 Finding Surface Area of a Prism STO: NJ 4.2.E.2TOP: 10-3 Example 1KEY: surface area of a prism,prism,surface area,net,multi-part questionMSC: NAEP M1j, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

46. ANS:a.

6 m

10 m

6 m 6 m17 m

8 m

b. 456 m

DIF: L1 REF: 10-3 Surface Areas of Prisms and CylindersOBJ: 10-3.1 Finding Surface Area of a Prism STO: NJ 4.2.E.2TOP: 10-3 Example 1KEY: surface area of a prism,prism,surface area,net,multi-part questionMSC: NAEP M1j, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

ESSAY

47. ANS:[4] B is the midpoint of AC, D is the midpoint of CE, and F is the midpoint of AE.

By the Triangle Midsegment Theorem:

By the definition of midpoint: By substituting,FA = BD and AB = DF. Since FB = FB , by SSS.

[3] correct idea, some details inaccurate[2] correct idea, not well organized[1] correct idea, one or more significant steps omitted

DIF: L3 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments STO: NJ 4.2.A.3KEY: paragraph proof,proof,reasoning,extended response,rubric-based question,Triangle Midsegment Theorem,midsegmentMSC: NAEP G3f, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

48. ANS:[4] BC = 13 by the Perpendicular Bisector Theorem.

AE = 5 by the Perpendicular Bisector Theorem.BE = 12 by the Perpendicular Bisector Theorem, so DB = DE + BE = 12 + 12 = 24.

by SAS, so DC = BC = 13.[3] finds three lengths with correct explanations[2] finds two lengths with correct explanations

[1] finds one length with correct explanation

DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3KEY: extended response,rubric-based question,reasoning,perpendicular bisector,Perpendicular Bisector TheoremMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

49. ANS:[4] Shows enough properties that do not require angle measurement and concludes, based

on those properties, that the quadrilateral is a rectangle. Sample: Measure to show diagonals bisect each other. This makes the quadrilateral a parallelogram. Measure to show that diagonals are congruent. This makes the parallelogram a rectangle.

[3] demonstrates understanding of exercise, but omits one property needed to conclude quadrilateral is parallelogram

[2] gives way of determining that quadrilateral is rectangle, but includes angle measurement (such as making right angles)

[1] gives only one step necessary for concluding quadrilateral is rectangle

DIF: L3 REF: 6-4 Special ParallelogramsOBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? STO: NJ 4.2.A.3TOP: 6-4 Example 4KEY: rectangle,writing in math,reasoning,extended response,rubric-based questionMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

50. ANS:

[4] Answers may vary. Sample:The height of the ladder by the first building is

The height of the ladder by the second building is

The second ladder goes about 2 feet higher than the first ladder.[3] correct methods, but error in computation[2] error in method used[1] correct answer but work not shown

DIF: L2 REF: 7-2 The Pythagorean Theorem and Its ConverseOBJ: 7-2.1 The Pythagorean Theorem STO: NJ 4.2.A.1, NJ 4.2.E.1TOP: 7-2 Example 3KEY: Pythagorean Theorem,extended response,rubric-based question,word problem,problem solving

MSC: NAEP G3d, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52

51. ANS:

[4] Answers may vary. Sample: If a basketball has a circumference of 30, then its diameter

is . If the ball goes in exactly in the center of the rim, then there is a total of (18 – 9.549) inches or 8.551 inches on both sides of the ball. Therefore, there is half of this distance, or about 4.2 inches, between the ball and the rim.

[3] correct methods used, but with a computational error[2] error in method[1] correct answer with no work shown

DIF: L2 REF: 7-6 Circles and Arcs OBJ: 7-6.2 Circumference and Arc LengthSTO: NJ 4.2.A.1, NJ 4.2.A.3 TOP: 7-6 Example 4KEY: circumference,diameter,extended response,rubric-based questionMSC: NAEP M1h, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

52. ANS:[4] Answers may vary. Sample: The total length of wrought iron used is the sum of the

outer circumference plus the inner circumference plus the eleven segments.

The length of wrought iron used is approximately 59 meters.[3] correct methods used, but with computational error[2] error in method[1] correct answer with no work shown

DIF: L2 REF: 7-6 Circles and Arcs OBJ: 7-6.2 Circumference and Arc LengthSTO: NJ 4.2.A.1, NJ 4.2.A.3 TOP: 7-6 Example 5KEY: circumference,concentric circles,extended response,rubric-based question,word problem,problem solvingMSC: NAEP M1h, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S10.TSK2.GM, TV.LV20.13, TV.LV20.14

53. ANS:[4] a. Use the formula for lateral area.

L.A. = Use the formula for the lateral area of a cylinder.= Substitute.

1979 Use a calculator.The lateral area is about 1979 square centimeters.

b. Use the formula for the lateral area of a cylinder plus one base, or circle.

Substitute the known values and solve for r.L.A. +

area of one circle

=

3000 = Substitute.3000 = Simplify and factor.

= Divide each side by .

955 Divide and approximate.

You now have the equation r + 100r – 955 = 0. Since this is not factorable, you need to use the quadratic formula to solve for r.

Quadratic Formula

a = 1, b = 50, c = –955

Simplify.

You can disregard the second value since it will be negative, so the radius is about 8.8 cm.

[3] one mathematical error or correct answers with incomplete explanations[2] two mathematical errors or correct answers with errors in explanation[1] correct answers with no explanation

DIF: L3 REF: 10-3 Surface Areas of Prisms and CylindersOBJ: 10-3.2 Finding Surface Area of a Cylinder STO: NJ 4.2.E.2KEY: cylinder,surface area of a cylinder,lateral area,word problem,problem solving,surface area formulas,surface area,rubric-based question,extended responseMSC: NAEP M1j, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

54. ANS:[4] a. To find the actual dimensions, you must use the scale of 1 cm to 0.5 meters. A

quick way to find the dimensions is to divide each value of a measure by 2 and then that is the number of meters in the dimension for the cabin.

14 ÷ 2 = 7, so this is 7 meters.20 ÷ 2 = 10, so this is 10 meters.7 ÷ 2 = 3.5, so this is 3.5 meters.

The dimensions of the actual cabin are 7 m by 10 m by 3.5 m.b. To find the volume of the cabin, use the formula for volume of a prism.

V = Bh Use the formula for volume.== 245

The volume of the cabin is 245 cubic meters.c. To find the ratio, you must know the volume of each cabin in the same units. The

volume of the model is cubic centimeters. The volume of the actual cabin is

= 245,000,000 cubic centimeters, since each meter is 100 centimeters.

The ratio of the volumes is 1 to 125,000.[3] one mathematical error or correct answers with incomplete explanations[2] two mathematical errors or correct answers with errors in explanation[1] correct answers with no explanation

DIF: L2 REF: 10-5 Volumes of Prisms and CylindersOBJ: 10-5.1 Finding Volume of a Prism STO: NJ 4.2.E.2KEY: extended response,volume of a rectangular prism,prism,problem solving,word problem,rubric-based question,volume formulas,volumeMSC: NAEP M1j, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16, TV.LV20.17

55. ANS:[4] Think of the balloon at its two different sizes as two similar solids. The ratio of the

small balloon to the large balloon is 5 to 10 or 1 to 2. If the ratio of the solids is 1 to 2, then the ratio of the volumes will be 1 to 2 , or 1 to 8. Write and solve a proportion to find the larger volume.

= Write a proportion.

x = 8(71) Write the cross products.x = 568 Multiply.

The volume of the balloon when the design is 10 cm wide is 568 cm .[3] one mathematical error or correct computation with incomplete explanations[2] two mathematical errors or correct computations with errors in explanation[1] correct answer with no explanation

DIF: L2 REF: 10-8 Areas and Volumes of Similar SolidsOBJ: 10-8.1 Finding Relationships in Area and Volume STO: NJ 4.2.E.2KEY: similarity ratio,extended response,problem solving,word problem,volumes of similar solids,rubric-based questionMSC: NAEP M2g, CAT5.LV20.50, CAT5.LV20.51, CAT5.LV20.52, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.NS, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.NS, S10.TSK2.PRA, TV.LV20.10, TV.LV20.13, TV.LV20.14, TV.LV20.52

OTHER

56. ANS:The inverse and converse are contrapositives of each other.

DIF: L3 REF: 5-4 Inverses¸ Contrapositives¸ and Indirect ReasoningOBJ: 5-4.1 Writing the Negation¸ Inverse¸ and Contrapositive STO: NJ 4.2.A.4KEY: equivalent statements,contrapositive,inverse,converse,reasoningMSC: NAEP G5a, CAT5.LV20.54, IT.LV16.CP, IT.LV16.PS, S9.TSK2.PRA, S10.TSK2.PRA, TV.LV20.16, TV.LV20.17

57. ANS:The net; the net is the perpendicular bisector of the segment joining the midpoints of the two baselines. By the Perpendicular Bisector Theorem, any point on the net is equidistant from the midpoints of the two baselines.

DIF: L1 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors STO: NJ 4.2.A.3TOP: 5-2 Example 1KEY: Perpendicular Bisector Theorem,perpendicular bisector,reasoning,writing in mathMSC: NAEP G3b, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.14, TV.LV20.16

58. ANS: by the definition of rhombus. by the Reflexive Property, so

by SSS.

DIF: L1 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals STO: NJ 4.2.A.3KEY: reasoning,writing in math,rhombus,diagonalMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.12, TV.LV20.14, TV.LV20.16

59. ANS:

Yes. is supplementary to both and since 41 + 139 = 180. So and ABCD is a parallelogram.

DIF: L2 REF: 6-3 Proving That a Quadrilateral is a ParallelogramOBJ: 6-3.1 Is the Quadrilateral a Parallelogram? STO: NJ 4.2.A.3KEY: parallelogram,reasoning,writing in mathMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16, TV.LV20.17, TV.LV20.18

60. ANS:Yes; the sum of the angle measures of a quadrilateral is 360. If all angles are congruent, each angle would have measure 90, so the figure would be a parallelogram (a rectangle, in fact).

DIF: L2 REF: 6-4 Special ParallelogramsOBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? STO: NJ 4.2.A.3TOP: 6-4 Example 3 KEY: parallelogram,rectangle,reasoning,writing in mathMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

61. ANS:Yes; the quadrilateral could be a parallelogram. Tick marks are used to show congruent segments. Different tick marks do not mean different lengths. If the quadrilateral were a parallelogram, the two sides with different tick marks would be congruent.

DIF: L3 REF: 6-4 Special ParallelogramsOBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? STO: NJ 4.2.A.3TOP: 6-4 Example 3 KEY: parallelogram,writing in math,reasoningMSC: NAEP G3f, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.16

62. ANS:Answers may vary. Sample:

It is a right triangle because the sum of the squares of the shorter two sides equals the square of the longest side.

DIF: L2 REF: 7-2 The Pythagorean Theorem and Its ConverseOBJ: 7-2.2 The Converse of the Pythagorean Theorem STO: NJ 4.2.A.1, NJ 4.2.E.1TOP: 7-2 Example 5 KEY: right triangle,Pythagorean Theorem,reasoningMSC: NAEP G3d, CAT5.LV20.50, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, S9.TSK2.GM, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.52

63. ANS:a. To find the volume of the cylinder, use the formula. You need to use the height and the

radius of the cylinder. The radius is the radius of the ball or . The height of the cylinder is since 3 balls occupy the cylinder.

V = Use the formula for the volume of a cylinder.V = Substitute 6.5 for r and 39 for h.V 5177 Use a calculator.

The volume of the cylinder is about 5177 cm .b. Use the formula for volume of a sphere to find the volume of one sphere. Then

multiply the result by 3.

V = Use the formula for the volume of a sphere.

V = Substitute 6.5 for r.

V 1150 Use a calculator.The volume of the three balls is about cm , or 3450 cm .

c. To find the percent of the cylinder’s volume occupied by the balls, write a fraction with the volume of the balls as the numerator and the volume of the cylinder as the denominator. Then write the fraction as a percent.

DIF: L3 REF: 10-7 Surface Areas and Volumes of SpheresOBJ: 10-7.1 Finding Surface Area and Volume of a Sphere STO: NJ 4.2.E.2KEY: cylinder,volume of a cylinder,volume of a sphere,multi-part question,problem solving,sphere,volume formulas,volume,writing in mathMSC: NAEP M1j, CAT5.LV20.46, CAT5.LV20.51, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.NS, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.NS,

S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.18, TV.LV20.5264. ANS:

If the value for the volume is the same as the value for the surface area then it means that , since the radius is the same and these are the two formulas that Katie would have used. Solve this equation for r.

= Divide each side by .

= Simplify.

== Divide each side by r .

4 = Simplify.

=Multiply each side by .

3 = r Simplify.

The radius of the ball is 3 inches.

DIF: L3 REF: 10-7 Surface Areas and Volumes of SpheresOBJ: 10-7.1 Finding Surface Area and Volume of a Sphere STO: NJ 4.2.E.2KEY: volume of a sphere,surface area of a sphere,problem solving,sphere,surface area,surface area formulas,volume formulas,volume,writing in mathMSC: NAEP M1j, CAT5.LV20.46, CAT5.LV20.51, CAT5.LV20.55, CAT5.LV20.56, IT.LV16.AM, IT.LV16.CP, IT.LV16.PS, S9.TSK2.GM, S9.TSK2.NS, S9.TSK2.PRA, S10.TSK2.GM, S10.TSK2.NS, S10.TSK2.PRA, TV.LV20.13, TV.LV20.14, TV.LV20.18, TV.LV20.52