geometry final exam review - mendham borough …€¦ · geometry final exam review multiple choice...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry Final Exam Review

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Based on the pattern, what is the next figure in the sequence?

a. b. c. d.

____ 2. 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 5

b. 2 and 2

c. A counterexample exists, but it is not shown above.

d. There is no counterexample. The conjecture is true.

____ 3. Name the ray that is opposite BA→

.

a. BD→

b. BA→

c. CA→

d. DA→

____ 4. Find AC.

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

Name: ________________________ ID: A

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____ 5. In the figure shown, m∠AED = 120. Which of the following statements is false?

Not drawn to scale

a. m∠AEB = 60

b. ∠BEC and ∠CED are adjacent angles.

c. m∠BEC = 120

d. ∠AED and ∠BEC are adjacent angles.

____ 6. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?

a. about 10 miles c. about 8 miles

b. about 50 miles d. about 40 miles

____ 7. Find the perimeter of the rectangle. The drawing is not to scale.

a. 151 feet b. 208 feet c. 161 feet d. 104 feet

Name: ________________________ ID: A

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____ 8. Find the perimeter of ∆ABC with vertices A(–5, –2), B(–2, –2), and C(–5, 2).

a. 12 units b. 7 units c. 32 units d. 14 units

____ 9. Find the area of a rectangle with base 2 yd and height 5 ft.

a. 10 yd2

b. 30 ft2

c. 10 ft2

d. 30 yd2

____ 10. Find the area of the circle in terms of π.

a. 30π in.2 b. 900π in.2 c. 60π in.2 d. 225π in.2

____ 11. If the perimeter of a square is 72 inches, what is its area?

a. 72 in.2

b. 324 in.2

c. 18 in.2

d. 5,184 in.2

Name: ________________________ ID: A

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____ 12. Jennifer has 78 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Jennifer

the garden with greatest area? The diagrams are not to scale.

a. c.

b. d.

____ 13. 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.

Name: ________________________ ID: A

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____ 14. Draw a Draw a Venn diagram to illustrate this conditional:

Cars are motor vehicles.

a. c.

b. d.

____ 15. Which choice shows a true conditional with the hypothesis and conclusion identified correctly?

a. Yesterday was Monday if tomorrow is Thursday.

Hypothesis: Tomorrow is Thursday.

Conclusion: Yesterday was Monday.

b. If tomorrow is Thursday, then yesterday was Tuesday.

Hypothesis: Yesterday was Tuesday.

Conclusion: Tomorrow is not Thursday.

c. If tomorrow is Thursday, then yesterday was Tuesday.

Hypothesis: Yesterday was Tuesday.

Conclusion: Tomorrow is Thursday.

d. Yesterday was Tuesday if tomorrow is Thursday.

Hypothesis: Tomorrow is Thursday.

Conclusion: Yesterday was Tuesday.

____ 16. 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.

Name: ________________________ ID: A

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____ 17. 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.

____ 18. One way to show that a statement is NOT a good definition is to find a ____.

a. converse c. biconditional

b. conditional d. counterexample

____ 19. 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

____ 20. 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 = 15

Name: ________________________ ID: A

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____ 21. Which statement is true?

a. ∠CBA and∠EBH are same-side angles.

b. ∠EBH and∠BED are same-side angles.

c. ∠CBA and ∠HBE are alternate interior angles.

d. ∠EBH and∠BED are alternate interior angles.

____ 22. Find the value of the variable if m Ä l, m∠1 = 2x + 44 and m∠5 = 5x + 38. The diagram is not to scale.

a. 1 b. 2 c. 3 d. –2

Name: ________________________ ID: A

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This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both

runways.

____ 23. How are ∠6 and ∠2 related?

a. corresponding angles c. same-side interior angles

b. alternate interior angles d. none of these

Name: ________________________ ID: A

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____ 24. Which is a correct two-column proof?

Given: ∠H and ∠C are supplementary.

Prove: j Ä l

a.

Statements Reasons

∠H and ∠C are supplementary. Given

∠H ≅ ∠E Vertical Angles

∠E and ∠C are supplementary. Substitution

j Ä l Same-Side Interior Angles Converse

b.

Statements Reasons


∠H ≅ ∠E Alternate Exterior Angles

∠G and ∠A are supplementary. Substitution


c.

Statements Reasons


∠H ≅ ∠E Vertical Angles

∠E and ∠C are supplementary. Same-Side Interior Angles


d. none of these

Name: ________________________ ID: A

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____ 25. Which lines, if any, can you conclude are parallel given that m∠1 + m∠2 = 180? Justify your conclusion

with a theorem or postulate.

a. j Ä k , by the Converse of the Same-Side Interior Angles Theorem

b. j Ä k , by the Converse of the Alternate Interior Angles Theorem

c. g Ä h , by the Converse of the Alternate Interior Angles Theorem

d. g Ä h , by the Converse of the Same-Side Interior Angles Theorem

____ 26. If c ⊥ b and a Ä c, what is m∠2?

a. 90 c. 74

b. 106 d. not enough information

____ 27. Classify the triangle by its sides. The diagram is not to scale.

a. straight b. scalene c. isosceles d. equilateral

____ 28. A triangular playground has angles with measures in the ratio 8 : 3 : 9. What is the measure of the smallest

angle?

a. 27 b. 3 c. 10 d. 30

Name: ________________________ ID: A

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____ 29. What is a correct name for the polygon?

a. EDCAB b. ABCDA c. CDEAB d. BAEAB

____ 30. Classify the polygon by its sides.

a. triangle b. hexagon c. pentagon d. octagon

____ 31. The chips used in the board game MathFuries have the shape of hexagons. How many sides does each

MathFuries chip have?

a. 5 b. 6 c. 8 d. 10

____ 32. Use less than, equal to, or greater than to complete the statement. The measure of each exterior angle of a

regular 7-gon is ____ the measure of each exterior angle of a regular 5-gon.

a. cannot tell b. equal to c. less than d. greater than

____ 33. Complete this statement. A polygon with all sides the same length is said to be ____.

a. regular b. equilateral c. equiangular d. convex

Name: ________________________ ID: A

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____ 34. Graph y = −3

4x – 1.

a. c.

b. d.

____ 35. Write an equation in point-slope form of the line through points (4, –4) and (1, 2). Use (4, –4) as the point

(x1, y1).

a. (y – 4) = –2(x + 4) c. (y + 4) = 2(x – 4)

b. (y – 4) = 2(x + 4) d. (y + 4) = –2(x – 4)

____ 36. At the curb a ramp is 11 inches off the ground. The other end of the ramp rests on the street 55 inches straight

out from the curb. Write a linear equation in slope-intercept form that relates the height y of the ramp to the

distance x from the curb.

a. y = 5x + 11 c. y = −1

5x + 55

b. y = −1

5x + 11 d. y =

1

5x + 55

Name: ________________________ ID: A

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____ 37. Is the line through points P(0, 5) and Q(–1, 8) parallel to the line through points R(3, 3) and S(5, –1)?

Explain.

a. No, the lines have unequal slopes.

b. Yes; the lines are both vertical.

c. Yes; the lines have equal slopes.

d. No, one line has zero slope, the other has no slope.

____ 38. Is the line through points P(1, 9) and Q(9, 6) perpendicular to the line through points R(–6, 0) and S(–9, 8)?

Explain.

a. Yes; their slopes have product –1.

b. No, their slopes are not opposite reciprocals.

c. No; their slopes are not equal.

d. Yes; their slopes are equal.

____ 39. Write an equation for the line perpendicular to y = 2x – 5 that contains (–9, 6).

a. y – 6 = 2(x + 9) c. y – 9 = −1

2(x + 6)

b. x – 6 = 2(y + 9) d. y – 6 = −1

2(x + 9)

____ 40. Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = 3x – 3. A

perpendicular brace passes through the point (–7, 9). Write an equation of the line that contains the brace.

a. y – 7 = 1

3(x + 9) c. x – 9 = 3(y + 7)

b. y – 9 = 3(x + 7) d. y – 9 = −1

3(x + 7)

____ 41. What must be true about the slopes of two perpendicular lines, neither of which is vertical?

a. The slopes are equal.

b. The slopes have product 1.

c. The slopes have product –1.

d. One of the slopes must be 0.

____ 42. Give the slope-intercept form of the equation of the line that is perpendicular to

7x + 3y = 18 and contains P(6, 8).

a. y – 6 = 3

7(x – 8) c. y =

3

7x +

38

7

b. y = 3

7x +

18

7d. y – 8 =

3

7(x – 6)

Name: ________________________ ID: A

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____ 43. Construct the line perpendicular to KL at point M .

a. c.

b. d.

Name: ________________________ ID: A

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____ 44. Construct the line that is perpendicular to the given line through the given point.

a. c.

b. d.

____ 45. Given ∆ABC ≅ ∆PQR, m∠B = 3v + 4, and m∠Q = 8v − 6, find m∠B and m∠Q.

a. 22 b. 11 c. 10 d. 25

____ 46. Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?

a. either ASA or AAS c. AAS only

b. ASA only d. neither

Name: ________________________ ID: A

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____ 47. Based on the given information, what can you conclude, and why?

Given: ∠H ≅ ∠L, HJ ≅ JL

a. ∆HIJ ≅ ∆LKJ by ASA c. ∆HIJ ≅ ∆JLK by ASA

b. ∆HIJ ≅ ∆JLK by SAS d. ∆HIJ ≅ ∆LKJ by SAS

____ 48. R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m∠R = 60,

m∠S = 80, m∠F = 60, m∠D = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and

tell which segment is congruent to RT .

a. yes, by ASA; FD

b. yes, by AAS; ED

c. yes, by SAS; ED

d. No, the two triangles are not congruent.

____ 49. For which situation could you prove ∆1 ≅ ∆2 using the HL Theorem?

a. I only b. II only c. III only d. II and III

____ 50. BE→

is the bisector of ∠ABC and CD→

is the bisector of ∠ACB. Also, ∠XBA ≅ ∠YCA. Which of AAS, SSS,

SAS, or ASA would you use to help you prove BL ≅ CM ?

a. AAS b. SSS c. SAS d. ASA

Name: ________________________ ID: A

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____ 51. The legs of an isosceles triangle have lengths 2x + 4, x + 8. The base has length 5x − 2. What is the length of

the base?

a. 18 c. 12

b. 4 d. cannot be determined

____ 52. Find the value of x. The diagram is not to scale.

a. 32 b. 50 c. 64 d. 80

____ 53. Points B, D, and F are midpoints of the sides of ∆ACE. EC = 30 and DF = 23. Find AC. The diagram is not to

scale.

a. 30 b. 11.5 c. 60 d. 46

____ 54. The length of DE is shown. What other length can you determine for this diagram?

a. EF = 12 c. DF = 24

b. DG = 12 d. No other length can be determined.

Name: ________________________ ID: A

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____ 55. Q is equidistant from the sides of ∠TSR. Find the value of x. The diagram is not to scale.

a. 27 b. 3 c. 15 d. 30

____ 56. Find the center of the circle that you can circumscribe about the triangle.

a. (1

2, −1) b. (−1,

1

2) c. (–3,

1

2) d. (−1, –2)

____ 57. Where can the bisectors of the angles of an obtuse triangle intersect?

I. inside the triangle

II. on the triangle

III. outside the triangle

a. I only b. III only c. I or III only d. I, II, or II

Name: ________________________ ID: A

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____ 58. Find the length of AB, given that DB is a median of the triangle and AC = 26.

a. 13 c. 52

b. 26 d. not enough information

____ 59. For a triangle, list the respective names of the points of concurrency of

• perpendicular bisectors of the sides

• bisectors of the angles

• medians

• lines containing the altitudes.

a. incenter

circumcenter

centroid

orthocenter

b. circumcenter

incenter

centroid

orthocenter

c. circumcenter

incenter

orthocenter

centroid

d. incenter

circumcenter

orthocenter

centroid

____ 60. 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.

____ 61. Name the smallest angle of ∆ABC. The diagram is not to scale.

a. ∠A

b. ∠C

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

d. ∠B

Name: ________________________ ID: A

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____ 62. List the sides in order from shortest to longest. The diagram is not to scale.

a. LK , LJ , JK b. LJ , LK , JK c. LJ , JK , LK d. LK , JK , LJ

____ 63. 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 m

b. 11 m, 11 m, 12 m d. 21 m, 6 m, 10 m

____ 64. 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 23

b. at least 11 and at most 23 d. greater than 11 and less than 23

____ 65. Which statement is true?

a. All quadrilaterals are rectangles.

b. All quadrilaterals are squares.

c. All rectangles are quadrilaterals.

d. All quadrilaterals are parallelograms.

____ 66. WXYZ is a parallelogram. Name an angle congruent to ∠WZY.

a. ∠ZXY b. ∠XWZ c. ∠ZXW d. ∠WXY

Name: ________________________ ID: A

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____ 67. In the rhombus, m∠1 = 6x, m∠2 = x + y, and m∠3 = 18z. Find the value of each variable. The diagram is

not to scale.

a. x = 15, y = 165, z = 10 c. x = 15, y = 75, z = 5

b. x = 30, y = 75, z = 10 d. x = 30, y = 165, z = 5

____ 68. 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.

____ 69. Find m∠1 andm∠3 in the kite. The diagram is not to scale.

a. 51, 51 b. 39, 39 c. 39, 51 d. 51, 39

____ 70. m∠R = 130 and m∠S = 80. Find m∠T. The diagram is not to scale.

a. 65 b. 70 c. 35 d. 80

Name: ________________________ ID: A

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____ 71. Which diagram shows the most useful positioning and accurate labeling of a kite in the coordinate plane?

a. c.

b. d.

____ 72. The length of a rectangle is 61

2 inches and the width is 3

3

4 inches. What is the ratio, using whole numbers, of

the length to the width?

a. 26 : 15 b. 26 : 30 c. 15 : 26 d. 13 : 15

____ 73. If a

b=5

3, then 3a = ____.

a. 3b b. 10b c. 5b d. 6b

____ 74. If g

h=6

5, which equation must be true?

a. 5h = 6g b.h

g=5

6c.

h

6=g

5d. gh = 6 × 5

Solve the proportion.

____ 75. n − 6

3n=n − 5

3n + 1

a. –3 b.2

5c.

9

17d. 3

Name: ________________________ ID: A

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____ 76. Figure TQRS ∼ BCDE . Name a pair of corresponding sides?

a. TQ and BE b. TS and CD c. RS and BC d. QR and CD

____ 77. The two rectangles are similar. Which is a correct proportion for corresponding sides?

a.12

8=x

4b.

12

4=x

8c.

12

4=x

20d.

4

12=x

8

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

____ 78. In ∆RST, RS = 10, RT = 15, and m∠R = 32. In ∆UVW, UV = 12, UW = 18, and m∠U = 32.

a. ∆RST ∼ ∆WUV ; 5

6c. ∆RST ∼ ∆VWU ;

6

5

b. ∆RST ∼ ∆UVW ; 5

6 d. The triangles are not similar.

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.

____ 79. The pentagons are similar. Find the value of the variables.

a. x = 13, y = 4 c. x = 5.5, y = 10

b. x = 7, y = 2 d. x = 13, y = 6

____ 80. If one measurement of a golden rectangle is 8.8 inches, which could be the other measurement?

a. 14.238 in. b. 10.418 in. c. 7.182 in. d. 1.618 in.

Name: ________________________ ID: A

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____ 81. Are the triangles similar? If so, explain why.

a. yes, by SAS∼ b. yes, by SSS∼ c. yes, by AA∼ d. no

____ 82. Which group contains triangles that are all similar?

a.

b.

c.

d.

Name: ________________________ ID: A

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Solve for a and b.

____ 83.

a. a =400

21, b =

580

21c. a =

580

21, b =

29

21

b. a =400

21, b =

20

21d. a =

20

21, b =

580

21

____ 84. Given: PQ Ä BC . Find the length of AQ. The diagram is not drawn to scale.

a. 11 b. 12 c. 18 d. 9

____ 85. Given AE Ä BD , solve for x.The diagram is not drawn to scale.

a. 76

7b. 3

2

11c. 15

2

5d. 26

2

5

Name: ________________________ ID: A

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Solve for x.

____ 86.

a. 5 b. 2.5 c. 7.5 d. 10

____ 87. Find x to the nearest tenth.

a. 4.8 b. 14.4 c. 9.4 d. 1.7

____ 88. Four explorers are trying to find the distance across an oddly shaped lake. They position themselves as shown

in the diagram. Alhombra uses her compass to instruct Chou and Duong to move along the line they form

with Bizet until she sees that from her perspective the angle between Bizet and Chou is equal to the angle

formed between Chou and Duong. They measure the distance between Bizet and Chou to be 35 m, between

Chou and Duong to be 46 m, and between Alhombra and Duong to be 100 m. How long is the lake from east

to west? Round your answer to the nearest tenth of a meter.

a. 76.1 m b. 77.4 m c. 131.4 m d. 132.4 m

____ 89. An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A

second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of

the triangle. Round answers to the nearest tenth of a centimeter.

a. 41.4 cm, 8.3 cm c. 41.4 cm, 4.3 cm

b. 30 cm, 5.8 cm d. 8.3 cm, 5.8 cm

Name: ________________________ ID: A

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____ 90. Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to

the nearest tenth.

a. x = 7, y = 9.9 b. x = 9.9, y = 7 c. x = 4.9, y = 6.1 d. x = 6.1, y = 4.9

Find the value of x. Round your answer to the nearest tenth.

____ 91.

a. 6.2 cm b. 12.7 cm c. 15.5 cm d. 10.9 cm

Find the value of x. Round to the nearest tenth.

____ 92.

a. 10.3 b. 31.4 c. 10.7 d. 31.8

Name: ________________________ ID: A

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____ 93. A slide 4.1 meters long makes an angle of 35° with the ground. To the nearest tenth of a meter, how far above

the ground is the top of the slide?

a. 7.1 m b. 3.4 m c. 5.0 m d. 2.4 m

Use compass directions to describe the direction of the vector.

(Not drawn to scale)

____ 94.

a. 43° east of north c. 43° west of south

b. 43° east of south d. 43° west of north

Name: ________________________ ID: A

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____ 95.

a. 84° north of west c. 84° south of east

b. 84° south of west d. 84° north of east

____ 96. A glider lands 17 miles west and 9 miles south from where it took off. The result of the trip can be described

by the vector −17⟨ , −9⟩. Use distance (for magnitude) and direction to describe this vector a second way.

a. about 19 miles at 28° south of west c. about 19 miles at 28° north of west

b. about 28 miles at 19° north of west d. about 28 miles at 19° south of west

Write the sum of the two vectors as an ordered pair.

____ 97. 5⟨ , −2⟩ and 0⟨ , 0⟩

a. 0⟨ , 0⟩ b. −5⟨ , 2⟩ c. 10⟨ , −4⟩ d. 5⟨ , −2⟩

____ 98. −6⟨ , 5⟩ and 6⟨ , −5⟩

a. 0⟨ , 0⟩ b. −12⟨ , −10⟩ c. 12⟨ , 10⟩ d. 1⟨ , 1⟩

Name: ________________________ ID: A

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____ 99. Which of these transformations are isometries?

(I) parallelogram EFGH → parallelogram XWVU

(II) hexagon CDEFGH → hexagon YXWVUT

(III) triangle EFG → triangle VWU

a. I only b. II and III only c. I and III only d. I, II, and III

Name: ________________________ ID: A

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____ 100. Which graph shows a triangle and its reflection image in the x-axis?

a. c.

b. d.

____ 101. Write a rule to describe the transformation that is a reflection in the x-axis.

a. (x, y) → (y, x) c. (x, y) → (–x, –y)

b. (x, y) → (–x, y) d. (x, y) → (x, –y)

Name: ________________________ ID: A

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The hexagon GIKMPR and ∆FJN are regular. The dashed line segments form 30° angles.

____ 102. Find the image of point P after a rotation of 240° about point M .

a. G b. O c. R d. K

____ 103. Find the glide reflection image of the upper right triangle for the glide of −8, − 7 and reflection line x = −3.

a. c.

b. d.

Name: ________________________ ID: A

33

____ 104. The right figure is an isometry of the left figure. Tell whether their orientations are the same or opposite.

Then classify the isometry.

a. opposite orientation; reflection

b. opposite orientation; translation

c. same orientation; rotation

d. same orientation; glide reflection

____ 105. Tell whether the three-dimensional object has rotational symmetry about a line and/or reflectional symmetry

in a plane.

a. reflectional symmetry

b. reflectional symmetry and rotational symmetry

c. rotational symmetry

d. no symmetry

____ 106. Which regular polygon can be used to form a tessellation? The sum of the measures of the angles of each

polygon is given.

a. octagon; 1080° b. nonagon; 1260° c. triangle; 180° d. decagon; 1440°

____ 107. Which figure can be used to make a pure tessellation?

a. b. c. d.

Name: ________________________ ID: A

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____ 108. Which tessellation has rotational symmetry and translational symmetry, but no other types of symmetry?

a. c.

b. d.

____ 109. The dashed triangle is a dilation image of the solid triangle. What is the scale factor?

a.1

4b.

1

2c.

2

3d. 2

Name: ________________________ ID: A

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Find the area. The figure is not drawn to scale.

____ 110.

a. 10.8 cm2 b. 5.4 cm2 c. 21.6 cm2 d. 7.4 cm2

____ 111.

a. 30 yd2 b. 6.5 yd2 c. 13 yd2 d. 15 yd2

____ 112.

a. 188 in.2 b. 278 in.2 c. 322 in.2 d. none of these

____ 113. The area of a parallelogram is 420 cm2 and the height is 35 cm. Find the corresponding base.

a. 385 cm b. 455 cm c. 14,700 cm2 d. 12 cm

____ 114. Find the area of a polygon with the vertices of (–2, 3), (1, 3), (5, –3), and (–2, –3).

a. 120 units2 b. 7 units2 c. 30 units2 d. 60 units2

Name: ________________________ ID: A

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Find the area of the trapezoid. Leave your answer in simplest radical form.

____ 115.

a. 98 cm2 b. 91 cm2 c. 38.5 cm2 d. 11 cm2

____ 116. Find the area of an equilateral triangle with radius 8 3 m. Leave your answer in simplest radical form.

a. 96 3 m2 b. 144 3 m2 c. 18 3 m2 d. 12 3 m2

____ 117. The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the perimeters? Of the areas?

a. 8 : 7 and 64 : 49 c. 9 : 8 and 81 : 64

b. 9 : 8 and 64 : 49 d. 8 : 7 and 81 : 64

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest

whole number.

____ 118. Find the similarity ratio and the ratio of perimeters for two regular octagons with areas of 18 in.2 and 50 in.

2.

a. 3 : 5; 3: 5 b. 9 : 25; 3 : 5 c. 3 : 5; 9 : 25 d. 9 : 25; 9 : 25

Find the area of the regular polygon. Give the answer to the nearest tenth.

____ 119. pentagon with radius 8 m

a. 304.3 m2

b. 152.2 m2

c. 30.4 m2

d. 154.2 m2

____ 120. A gardener needs to cultivate a triangular plot of land. One angle of the garden is 47 °, and two sides adjacent

to the angle are 77 feet and 76 feet. To the nearest tenth, what is the area of the plot of land?

a. 2163.5 ft2

b. 2139.9 ft2

c. 4279.9 ft2

d. 1995.5 ft2

____ 121. A park in a subdivision is triangular-shaped. Two adjacent sides of the park are 573 feet and 536 feet. The

angle between the sides is 58°. To the nearest unit, find the area of the park in square yards.

a. 32,557 yd2

b. 14,470 yd2

c. 28,940 yd2

d. 43,410 yd2

Name: ________________________ ID: A

37

____ 122. Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle.

Leave your answer in terms of π .

a. (4 − π ) in.2 b. 4 −1

2π

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃̃ in.2 c. 4 −

π

4

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃̃ in.2 d. π in.2

Find the area of the circle. Leave your answer in terms of π .

____ 123. The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round

to the nearest tenth.

a. 75.4 m2 b. 52.5 m2 c. 278.7 m2 d. 22.9 m2

Name: ________________________ ID: A

38

____ 124. What is the probability that a point chosen at random on the grid will lie in the unshaded region?

a.5

8b.

2

5c.

3

8d.

3

5

____ 125. Pierre built the model shown in the diagram below for a social studies project. He wants to be able to show

the inside of his model, so he sliced the figure as shown. Describe the cross section he created.

a. hexagon b. pentagon c. pyramid d. rectangle

Use formulas to find the lateral area and surface area of the given prism. Show your answer to the

nearest whole number.

____ 126.

a. 1045 m2; 1081 m

2c. 1045 m

2; 1117 m

2

b. 1009 m2; 1117 m

2d. 1009 m

2; 1189 m

2

Name: ________________________ ID: A

39

Find the surface area of the pyramid shown to the nearest whole number.

____ 127.

a. 85 ft2

b. 145 ft2

c. 60 ft2

d. 25 ft2

____ 128. Find the slant height x of the pyramid shown to the nearest tenth.

a. 2.4 mm b. 5 mm c. 2.6 mm d. 4.3 mm

____ 129. Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of

6 in.

a. 210 in.2

b. 240 in.2

c. 42 in.2

d. 420 in.2

Name: ________________________ ID: A

40

____ 130. Find the slant height of the cone to the nearest whole number.

a. 21 m b. 19 m c. 22 m d. 24 m

____ 131. Find the lateral area of the cone to the nearest whole number.

Not drawn to scale

a. 7540 m2

b. 3770 m2

c. 4712 m2

d. 9425 m2

Find the volume of the given prism. Round to the nearest tenth if necessary.

____ 132.

a. 2143.4 yd3

b. 1750.1 yd3

c. 4286.8 yd3

d. 2475.0 yd3

Name: ________________________ ID: A

41

Find the volume of the cylinder in terms of π .

____ 133.


____ 134.

h = 6 and r = 3


Find the volume of the cone shown as a decimal rounded to the nearest tenth.

____ 135.

a. 207.3 in.3

b. 1866.1 in.3

c. 5598.3 in.3

d. 2799.2 in.3

Name: ________________________ ID: A

42

____ 136.

a. 552.9 m3

b. 829.4 m3

c. 1,244.1 m3

d. 3,317.5 m3

Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure.

____ 137.

a. yes; 1 : 3 b. yes; 1 : 2 c. yes; 1 : 5 d. no

In the figure, PA→

and PB→

are tangent to circle O and PD→

bisects ∠BPA. The figure is not drawn to

scale.

____ 138. For m∠AOC = 46, find m∠POB.

a. 23 b. 90 c. 46 d. 68

Name: ________________________ ID: A

43

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to

scale.

____ 139. FG ⊥ OP, RS ⊥ OQ , FG = 40, RS = 37, OP = 19

a. 27.2 b. 18.5 c. 19 d. 20.5

____ 140.

a. 19.34 b. 10.49 c. 110 d. 9.22

Name: ________________________ ID: A

44

____ 141. The radius of circle O is 18, and OC = 13. Find AB. Round to the nearest tenth, if necessary. (The figure is

not drawn to scale.)

a. 12.4 b. 3.8 c. 24.9 d. 44.4

____ 142. m∠R = 22. Find m∠O. (The figure is not drawn to scale.)

a. 68 b. 22 c. 158 d. 44

Name: ________________________ ID: A

45

____ 143. Given that ∠DAB and ∠DCB are right angles and m∠BDC = 41, what is the measure of arc CAD? (The

figure is not drawn to scale.)

a. 164 b. 303 c. 246 d. 262

____ 144. Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.)

a. a = 53° b. b = 106° c. c = 73° d. d = 37°

____ 145. Find x. (The figure is not drawn to scale.)

a. 92 b. 44 c. 23 d. 46

Name: ________________________ ID: A

46

____ 146. Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to scale.)

a. 35.5° b. 58.5° c. 71° d. 21°

____ 147. m∠S = 36, m(arc RS) = 118, and RU is tangent to the circle at R. Find m∠U.

(The figure is not drawn to scale.)

a. 23 b. 82 c. 46 d. 41

____ 148. Find the diameter of the circle for BC = 16 and DC = 28. Round to the nearest tenth.

(The diagram is not drawn to scale.)

a. 33 b. 49 c. 14.3 d. 65

Name: ________________________ ID: A

47

____ 149. Write the standard equation of the circle in the graph.

a. (x + 3)2 + (y – 2)

2 = 9 c. (x – 3)

2 + (y + 2)

2 = 18

b. (x – 3)2 + (y + 2)

2 = 9 d. (x + 3)

2 + (y – 2)

2 = 18

Describe the locus in space.

____ 150. points 3 in. from plane K

a. a circle of radius 3 cm, centered at K

b. two planes parallel to plane K, each 3 in. from K

c. two lines parallel to plane K, each 3 in. from K

d. a sphere of radius 3 cm, centered at K

ID: A

1

Geometry Final Exam Review

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: L2

REF: 1-1 Patterns and Inductive Reasoning OBJ: 1-1.1 Using Inductive Reasoning

NAT: NAEP 2005 G5a STA: NJ 4.3.12 A.1 | NJ 4.3.12 A.3

TOP: 1-1 Example 1 KEY: pattern | inductive reasoning


REF: 1-1 Patterns and Inductive Reasoning OBJ: 1-1.1 Using Inductive Reasoning

NAT: NAEP 2005 G5a STA: NJ 4.3.12 A.1 | NJ 4.3.12 A.3

TOP: 1-1 Example 3 KEY: counterexample | conjecture

3. ANS: A PTS: 1 DIF: L2

REF: 1-4 Segments, Rays, Parallel Lines and Planes

OBJ: 1-4.1 Identifying Segments and Rays NAT: NAEP 2005 G3g

STA: NJ 4.2.12 A.1 | NJ 4.2.12 A.3a TOP: 1-4 Example 1

KEY: ray | opposite rays

4. ANS: C PTS: 1 DIF: L2 REF: 1-5 Measuring Segments

OBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1

STA: NJ 4.1.12 B.1 TOP: 1-5 Example 1

KEY: segment | segment length

5. ANS: D PTS: 1 DIF: L2 REF: 1-6 Measuring Angles

OBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 TOP: 1-6 Example 5

KEY: adjacent angles | supplementary angles | vertical angles

6. ANS: D PTS: 1 DIF: L3 REF: 1-8 The Coordinate Plane

OBJ: 1-8.1 Finding Distance on the Coordinate Plane

NAT: NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 C.1a | NJ 4.2.12 C.1b

KEY: coordinate plane | Distance Formula | word problem | problem solving


REF: 1-9 Perimeter, Circumference, and Area

OBJ: 1-9.1 Finding Perimeter and Circumference

NAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.2.12 C.1b

TOP: 1-9 Example 1 KEY: perimeter | rectangle


REF: 1-9 Perimeter, Circumference, and Area

OBJ: 1-9.1 Finding Perimeter and Circumference



TOP: 1-9 Example 3 KEY: perimeter | triangle | coordinate plane | Distance Formula

ID: A

2


REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.2 Finding Area



TOP: 1-9 Example 4 KEY: area | rectangle

10. ANS: D PTS: 1 DIF: L2




TOP: 1-9 Example 5 KEY: area | circle





KEY: area | square





KEY: rectangle | area | word problem | problem solving

13. ANS: D PTS: 1 DIF: L2 REF: 2-1 Conditional Statements

OBJ: 2-1.1 Conditional Statements NAT: NAEP 2005 G5a

STA: NJ 4.2.12 A.4c TOP: 2-1 Example 2

KEY: hypothesis | conclusion | conditional statement

14. ANS: A PTS: 1 DIF: L2 REF: 2-1 Conditional Statements



KEY: conditional statement | Venn Diagram

15. ANS: D PTS: 1 DIF: L3 REF: 2-1 Conditional Statements


STA: NJ 4.2.12 A.4c

KEY: conditional statement | truth value | hypothesis | conclusion

16. ANS: C PTS: 1 DIF: L2 REF: 2-1 Conditional Statements

OBJ: 2-1.2 Converses NAT: NAEP 2005 G5a


KEY: conditional statement | coverse of a conditional | truth value

17. ANS: B PTS: 1 DIF: L2 REF: 2-2 Biconditionals and Definitions

OBJ: 2-2.1 Writing Biconditionals NAT: NAEP 2005 G1c | NAEP 2005 G5a | ADP K.1.1


KEY: biconditional statement | conditional statement

18. ANS: D PTS: 1 DIF: L2 REF: 2-2 Biconditionals and Definitions

OBJ: 2-2.2 Recognizing Good Definitions

NAT: NAEP 2005 G1c | NAEP 2005 G5a | ADP K.1.1 STA: NJ 4.2.12 A.4c

KEY: counterexample

19. ANS: B PTS: 1 DIF: L2 REF: 2-3 Deductive Reasoning

OBJ: 2-3.1 Using the Law of Detachment NAT: NAEP 2005 G5a


KEY: deductive reasoning | Law of Detachment

ID: A

3

20. ANS: A PTS: 1 DIF: L2 REF: 2-5 Proving Angles Congruent

OBJ: 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.4c TOP: 2-5 Example 1

KEY: Vertical Angles Theorem | vertical angles | supplementary angles | multi-part question

21. ANS: D PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines

OBJ: 3-1.1 Identifying Angles NAT: NAEP 2005 M1f | ADP K.2.1

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4a TOP: 3-1 Example 1

KEY: same-side interior angles | alternate interior angles

22. ANS: B PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines

OBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1


KEY: corresponding angles | parallel lines |

23. ANS: A PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines

OBJ: 3-1.1 Identifying Angles NAT: NAEP 2005 M1f | ADP K.2.1


KEY: parallel lines | transversal | angle

24. ANS: A PTS: 1 DIF: L3 REF: 3-2 Proving Lines Parallel

OBJ: 3-2.1 Using a Transversal NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4a

TOP: 3-2 Example 1 KEY: parallel lines | reasoning | supplementary angles

25. ANS: A PTS: 1 DIF: L2 REF: 3-2 Proving Lines Parallel

OBJ: 3-2.1 Using a Transversal NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.3

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4a

TOP: 3-2 Example 1 KEY: parallel lines | reasoning


REF: 3-3 Parallel and Perpendicular Lines

OBJ: 3-3.1 Relating Parallel and Perpendicular Lines

NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1

STA: NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4a TOP: 3-3 Example 2

KEY: parallel lines | perpendicular lines | transversal


REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem

OBJ: 3-4.1 Finding Angle Measures in Triangles

NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4b

TOP: 3-4 Example 2

KEY: acute triangle | triangle | classifying triangles | scalene | isosceles triangle | equilateral


REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem

OBJ: 3-4.1 Finding Angle Measures in Triangles


STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.4b

KEY: triangle | angle

29. ANS: C PTS: 1 DIF: L2

REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.1 Classifying Polygons


STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.4b | NJ 4.3.12 A.3 | NJ 4.3.12 B.1 | NJ 4.3.12 C.1a | NJ

4.3.12 C.2 TOP: 3-5 Example 1 KEY: polygon

ID: A

4





4.3.12 C.2 TOP: 3-5 Example 2 KEY: classifying polygons





4.3.12 C.2 KEY: classifying polygons


REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums



4.3.12 C.2 KEY: sum of angles of a polygon


REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums



4.3.12 C.2 KEY: polygon | classifying polygons | equilateral

34. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane

OBJ: 3-6.1 Graphing Lines

NAT: NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2

STA: NJ 4.2.12 C.1b | NJ 4.3.12 B.1 | NJ 4.3.12 C.2 TOP: 3-6 Example 1

KEY: slope-intercept form | graphing

35. ANS: D PTS: 1 DIF: L2 REF: 3-6 Lines in the Coordinate Plane

OBJ: 3-6.2 Writing Equations of Lines


STA: NJ 4.2.12 C.1b | NJ 4.3.12 B.1 | NJ 4.3.12 C.2 TOP: 3-6 Example 5

KEY: point-slope form

36. ANS: B PTS: 1 DIF: L3 REF: 3-6 Lines in the Coordinate Plane

OBJ: 3-6.2 Writing Equations of Lines


STA: NJ 4.2.12 C.1b | NJ 4.3.12 B.1 | NJ 4.3.12 C.2

KEY: word problem | problem solving | slope-intercept form


REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: 3-7.1 Slope and Parallel Lines


STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 C.1b | NJ 4.2.12 C.1d | NJ 4.2.12 C.1e | NJ

4.3.12 C.1a | NJ 4.3.12 C.2 TOP: 3-7 Example 1

KEY: slopes of parallel lines | graphing | parallel lines


REF: 3-7 Slopes of Parallel and Perpendicular Lines

OBJ: 3-7.2 Slope and Perpendicular Lines




KEY: slopes of perpendicular lines | perpendicular lines

ID: A

5







KEY: slopes of perpendicular lines | perpendicular lines







KEY: word problem | problem solving | perpendicular lines | slopes of perpendicular lines






4.3.12 C.1a | NJ 4.3.12 C.2

KEY: slopes of perpendicular lines | perpendicular lines | reasoning






4.3.12 C.1a | NJ 4.3.12 C.2 KEY: slopes of perpendicular lines | perpendicular lines


REF: 3-8 Constructing Parallel and Perpendicular Lines

OBJ: 3-8.2 Constructing Perpendicular Lines

NAT: NAEP 2005 G3b | NAEP 2005 G3g | ADP K.2.1 | ADP K.2.2

STA: NJ 4.2.12 A.3a TOP: 3-8 Example 3

KEY: construction | perpendicular lines


REF: 3-8 Constructing Parallel and Perpendicular Lines

OBJ: 3-8.2 Constructing Perpendicular Lines

NAT: NAEP 2005 G3b | NAEP 2005 G3g | ADP K.2.1 | ADP K.2.2

STA: NJ 4.2.12 A.3a TOP: 3-8 Example 3

KEY: construction | perpendicular lines

45. ANS: C PTS: 1 DIF: L3 REF: 4-1 Congruent Figures

OBJ: 4-1.1 Congruent Figures NAT: NAEP 2005 G2e | ADP K.3

STA: NJ 4.2.12 A.1 | NJ 4.2.12 A.3b.a | NJ 4.2.12 A.4b

KEY: congruent figures | corresponding parts


REF: 4-3 Triangle Congruence by ASA and AAS

OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3

STA: NJ 4.2.12 A.1 | NJ 4.2.12 A.3b.a | NJ 4.2.12 A.4b TOP: 4-3 Example 3

KEY: ASA | AAS | reasoning

ID: A

6


REF: 4-3 Triangle Congruence by ASA and AAS

OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3


KEY: ASA | reasoning


REF: 4-4 Using Congruent Triangles: CPCTC

OBJ: 4-4.1 Proving Parts of Triangles Congruent NAT: NAEP 2005 G2e | ADP K.3


KEY: ASA | CPCTC | word problem

49. ANS: C PTS: 1 DIF: L3 REF: 4-6 Congruence in Right Triangles

OBJ: 4-6.1 The Hypotenuse-Leg Theorem NAT: NAEP 2005 G2e | ADP K.3


KEY: HL Theorem | right triangle | reasoning


REF: 4-7 Using Corresponding Parts of Congruent Triangles

OBJ: 4-7.1 Using Overlapping Triangles in Proofs NAT: NAEP 2005 G3f | ADP K.3


KEY: corresponding parts | congruent figures | ASA | SAS | AAS | SSS | reasoning


REF: 4-5 Isosceles and Equilateral Triangles

OBJ: 4-5.1 The Isosceles Triangle Theorems

NAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3b.a | NJ 4.2.12 A.4b

KEY: isosceles triangle | Isosceles Triangle Theorem | word problem | problem solving

52. ANS: C PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles

OBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3b.b | NJ 4.2.12 A.4b | NJ 4.2.12 C.1a |

NJ 4.2.12 C.1b | NJ 4.2.12 C.1d | NJ 4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 5-1 Example 1

KEY: midsegment | Triangle Midsegment Theorem

53. ANS: D PTS: 1 DIF: L2 REF: 5-1 Midsegments of Triangles

OBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3b.b | NJ 4.2.12 A.4b | NJ 4.2.12 C.1a |

NJ 4.2.12 C.1b | NJ 4.2.12 C.1d | NJ 4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 5-1 Example 1

KEY: midpoint | midsegment | Triangle Midsegment Theorem

54. ANS: A PTS: 1 DIF: L2 REF: 5-2 Bisectors in Triangles

OBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.4b TOP: 5-2 Example 1

KEY: perpendicular bisector | Perpendicular Bisector Theorem

55. ANS: B PTS: 1 DIF: L2 REF: 5-2 Bisectors in Triangles

OBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.4b TOP: 5-2 Example 2

KEY: angle bisector | Converse of the Angle Bisector Theorem


REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.1 Properties of Bisectors

NAT: NAEP 2005 G3b

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 C.1c

TOP: 5-3 Example 1 KEY: circumscribe | circumcenter of the triangle

ID: A

7


REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.1 Properties of Bisectors

NAT: NAEP 2005 G3b


KEY: incenter of the triangle | angle bisector | reasoning


REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes

NAT: NAEP 2005 G3b


TOP: 5-3 Example 3 KEY: median of a triangle


REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes

NAT: NAEP 2005 G3b


KEY: angle bisector | circumcenter of the triangle | centroid | orthocenter of the triangle | median | altitude |

perpendicular bisector


REF: 5-4 Inverses, Contrapositives, and Indirect Reasoning

OBJ: 5-4.1 Writing the Negation, Inverse, and Contrapositive NAT: NAEP 2005 G5a


KEY: contrapositive

61. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles

OBJ: 5-5.1 Inequalities Involving Angles of Triangles NAT: NAEP 2005 G3f

STA: NJ 4.1.12 A.2 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3b.c | NJ 4.2.12 A.4c

TOP: 5-5 Example 2 KEY: Theorem 5-10

62. ANS: C PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles

OBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3f


TOP: 5-5 Example 3 KEY: Theorem 5-11




TOP: 5-5 Example 4 KEY: Triangle Inequality Theorem




TOP: 5-5 Example 5 KEY: Triangle Inequality Theorem

65. ANS: C PTS: 1 DIF: L2 REF: 6-1 Classifying Quadrilaterals

OBJ: 6-1.1 Classifying Special Quadrilaterals NAT: NAEP 2005 G3f

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3c | NJ 4.2.12 C.1a | NJ 4.2.12 C.1b | NJ

4.2.12 C.1d | NJ 4.2.12 C.1e

KEY: reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals

66. ANS: D PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms

OBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a KEY: parallelogram | opposite angles

ID: A

8

67. ANS: C PTS: 1 DIF: L2 REF: 6-4 Special Parallelograms

OBJ: 6-4.1 Diagonals of Rhombuses and Rectangles NAT: NAEP 2005 G3f

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3c | NJ 4.2.12 A.4b

TOP: 6-4 Example 1 KEY: algebra | diagonal | rhombus | Theorem 6-13

68. ANS: B PTS: 1 DIF: L3 REF: 6-4 Special Parallelograms

OBJ: 6-4.2 Is the Parallelogram a Rhombus or a Rectangle? NAT: NAEP 2005 G3f

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3c | NJ 4.2.12 A.4b

TOP: 6-4 Example 3

KEY: square | reasoning | Theorem 6-10 | Theorem 6-11 | word problem | problem solving

69. ANS: C PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites

OBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3f

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4b

TOP: 6-5 Example 3 KEY: kite | Theorem 6-17 | diagonal

70. ANS: B PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites

OBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3f

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3c | NJ 4.2.12 A.4b

KEY: kite | sum of interior angles


REF: 6-6 Placing Figures in the Coordinate Plane OBJ: 6-6.1 Naming Coordinates

NAT: NAEP 2005 G4d

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3c | NJ 4.2.12 A.4b | NJ 4.2.12 C.1b | NJ 4.2.12 C.1d | NJ

4.3.12 D.3 KEY: algebra | coordinate plane | isosceles trapezoid | kite

72. ANS: A PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions

OBJ: 7-1.1 Using Ratios and Proportions

NAT: NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1

TOP: 7-1 Example 1 KEY: ratio

73. ANS: C PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions



TOP: 7-1 Example 2 KEY: proportion | Cross-Product Property

74. ANS: B PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions



TOP: 7-1 Example 2 KEY: Cross-Product Property | proportion

75. ANS: A PTS: 1 DIF: L3 REF: 7-1 Ratios and Proportions



TOP: 7-1 Example 3 KEY: proportion | Cross-Product Property

76. ANS: D PTS: 1 DIF: L2 REF: 7-2 Similar Polygons

OBJ: 7-2.1 Similar Polygons

NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 D.1

TOP: 7-2 Example 1 KEY: similar polygons | corresponding sides

77. ANS: B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons




TOP: 7-2 Example 1 KEY: similar polygons | corresponding sides

ID: A

9

78. ANS: B PTS: 1 DIF: L2 REF: 7-2 Similar Polygons




TOP: 7-2 Example 2

KEY: similar polygons | corresponding sides | corresponding angles

79. ANS: A PTS: 1 DIF: L3 REF: 7-2 Similar Polygons




TOP: 7-2 Example 3 KEY: corresponding sides | proportion

80. ANS: A PTS: 1 DIF: L2 REF: 7-2 Similar Polygons

OBJ: 7-2.2 Applying Similar Polygons



TOP: 7-2 Example 5 KEY: golden rectangle

81. ANS: C PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar

OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems

NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 D.1 | NJ 4.2.12 E.1a

TOP: 7-3 Example 2

KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity

Theorem

82. ANS: A PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar

OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems


STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 D.1 | NJ 4.2.12 E.1a

TOP: 7-3 Example 2

KEY: Angle-Angle Similarity Postulate | Side-Angle-Side Similarity Theorem | Side-Side-Side Similarity

Theorem

83. ANS: A PTS: 1 DIF: L3 REF: 7-4 Similarity in Right Triangles

OBJ: 7-4.1 Using Similarity in Right Triangles


STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3d | NJ 4.2.12 E.1a

TOP: 7-4 Example 2 KEY: corollaries of the geometric mean | proportion

84. ANS: D PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles

OBJ: 7-5.1 Using the Side-Splitter Theorem

NAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.3a | NJ 4.2.12 A.3d | NJ 4.2.12 D.1 | NJ 4.2.12 E.1a

TOP: 7-5 Example 1 KEY: Side-Splitter Theorem

85. ANS: A PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles





ID: A

10






87. ANS: B PTS: 1 DIF: L2 REF: 7-5 Proportions in Triangles

OBJ: 7-5.2 Using the Triangle-Angle-Bisector Theorem



TOP: 7-5 Example 3 KEY: Triangle-Angle-Bisector Theorem





TOP: 7-5 Example 3 KEY: Triangle-Angle-Bisector Theorem | word problem

89. ANS: D PTS: 1 DIF: L3 REF: 7-5 Proportions in Triangles




TOP: 7-5 Example 3 KEY: Triangle-Angle-Bisector Theorem

90. ANS: B PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles

OBJ: 8-2.1 45°-45°-90° Triangles NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 A.4a | NJ 4.2.12 D.1 | NJ 4.2.12 E.1b

TOP: 8-2 Example 2 KEY: special right triangles | hypotenuse | leg

91. ANS: A PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio

OBJ: 8-3.1 Using Tangents in Triangles

NAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 D.1 | NJ 4.2.12 E.1c

TOP: 8-3 Example 2 KEY: side length using tangent | tangent | tangent ratio

92. ANS: B PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios

OBJ: 8-4.1 Using Sine and Cosine in Triangles



TOP: 8-4 Example 2 KEY: sine | side length using since and cosine | sine ratio

93. ANS: D PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios

OBJ: 8-4.1 Using Sine and Cosine in Triangles



TOP: 8-4 Example 2

KEY: side length using since and cosine | word problem | problem solving | sine | sine ratio

94. ANS: D PTS: 1 DIF: L2 REF: 8-6 Vectors

OBJ: 8-6.1 Describing Vectors NAT: NAEP 2005 G4e | ADP I.4.1

STA: NJ 4.1.12 A.1 | NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.2.12 C.2 | NJ 4.2.12 C.2 | NJ

4.2.12 D.1 | NJ 4.2.12 E.1b | NJ 4.2.12 E.1c | NJ 4.3.12 D.3 TOP: 8-6 Example 2

KEY: initial point of a vector | terminal point of a vector | vector

ID: A

12

104. ANS: A PTS: 1 DIF: L2 REF: 9-6 Compositions of Reflections

OBJ: 9-6.2 Glide reflections NAT: NAEP 2005 G2d | ADP K.6


KEY: reflection | orientation | isometry

105. ANS: A PTS: 1 DIF: L2 REF: 9-4 Symmetry

OBJ: 9-4.1 Identifying types of symmetry in figures NAT: NAEP 2005 G2a | ADP K.6

STA: NJ 4.2.12 A.1 TOP: 9-4 Example 3

KEY: symmetry | rotational symmetry | reflectional symmetry

106. ANS: C PTS: 1 DIF: L2 REF: 9-7 Tessellations

OBJ: 9-7.1 Identifying transformations in tessellations NAT: NAEP 2005 G2a | ADP K.6


TOP: 9-7 Example 2 KEY: tessellation | tiling

107. ANS: B PTS: 1 DIF: L4 REF: 9-7 Tessellations

OBJ: 9-7.1 Identifying transformations in tessellations NAT: NAEP 2005 G2a | ADP K.6


KEY: tessellation | tiling | pure tessellation

108. ANS: B PTS: 1 DIF: L3 REF: 9-7 Tessellations

OBJ: 9-7.2 Identifying symmetries in tessellations NAT: NAEP 2005 G2a | ADP K.6


TOP: 9-7 Example 3

KEY: tessellation | tiling | transformation | rotational symmetry | translational symmetry

109. ANS: B PTS: 1 DIF: L2 REF: 9-5 Dilations

OBJ: 9-5.1 Locating dilation images NAT: NAEP 2005 G2c | ADP K.7


KEY: dilation | reduction | scale factor


REF: 10-1 Areas of Parallelograms and Triangles OBJ: 10-1.2 Area of a Triangle

NAT: NAEP 2005 M1h | ADP J.1.6 | ADP K.8.2

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 B.1 | NJ 4.2.12 E.2 | NJ 4.3.12 D.3

TOP: 10-1 Example 3 KEY: triangle | area





TOP: 10-1 Example 3 KEY: triangle | area





TOP: 10-1 Example 3 KEY: area | triangle | rectangle | parallelogram


REF: 10-1 Areas of Parallelograms and Triangles OBJ: 10-1.1 Area of a Parallelogram



TOP: 10-1 Example 1 KEY: area | base | height | parallelogram

ID: A

15



OBJ: 11-3.2 Finding Surface Area of a Cone



4.3.12 D.3 TOP: 11-3 Example 4

KEY: cone | slant height of a cone | Pythagorean Theorem



OBJ: 11-3.2 Finding Surface Area of a Cone



4.3.12 D.3 TOP: 11-3 Example 4

KEY: cone | surface area of a cone | surface area formulas | surface area


REF: 11-4 Volumes of Prisms and Cylinders OBJ: 11-4.1 Finding Volume of a Prism

NAT: NAEP 2005 M1j | ADP I.4.1 | ADP J.1.6 | ADP K.8.2


4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 11-4 Example 2

KEY: volume of a triangular prism | volume formulas | volume | prism


REF: 11-4 Volumes of Prisms and Cylinders

OBJ: 11-4.2 Finding Volume of a Cylinder



4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 11-4 Example 3

KEY: volume of a cylinder | cylinder | volume formulas | volume


REF: 11-4 Volumes of Prisms and Cylinders

OBJ: 11-4.2 Finding Volume of a Cylinder



4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 11-4 Example 3

KEY: volume of a cylinder | cylinder | volume formulas | volume | oblique cylinder


REF: 11-5 Volumes of Pyramids and Cones OBJ: 11-5.2 Finding Volume of a Cone



4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 11-5 Example 3

KEY: volume of a cone | oblique cone | volume formulas | volume


REF: 11-5 Volumes of Pyramids and Cones OBJ: 11-5.2 Finding Volume of a Cone



4.3.12 A.3 | NJ 4.3.12 D.3 TOP: 11-5 Example 4

KEY: volume of a cone | volume formulas | volume | cone

ID: A

17


REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.1 Finding Angle Measures



TOP: 12-4 Example 1

KEY: circle | secant | angle measure | arc measure | intersection inside the circle


REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.1 Finding Angle Measures



TOP: 12-4 Example 1

KEY: circle | chord | angle measure | arc measure | intersection on the circle | intersection outside the circle


REF: 12-4 Angle Measures and Segment Lengths OBJ: 12-4.2 Finding Segment Lengths



TOP: 12-4 Example 3

KEY: circle | intersection outside the circle | secant | tangent | diameter


REF: 12-5 Circles in the Coordinate Plane

OBJ: 12-5.2 Finding the Center and Radius of a Circle NAT: NAEP 2005 G4d | ADP K.10.4

STA: NJ 4.1.12 B.1 | NJ 4.2.12 A.1 | NJ 4.2.12 C.1a | NJ 4.3.12 B.1 | NJ 4.3.12 D.3

TOP: 12-4 Example 4

KEY: center | circle | coordinate plane | radius | equation of a circle

150. ANS: B PTS: 1 DIF: L2 REF: 12-6 Locus: A Set of Points

OBJ: 12-6.1 Drawing and Describing a Locus NAT: NAEP 2005 G1d

STA: NJ 4.2.12 A.2 TOP: 12-6 Example 3

KEY: locus

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