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GEOM. FINAL EXAM REVIEW PACKAGE

Multiple Choice

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

____ 1. ____ two points are collinear.

|a. |Any |b. |Sometimes |c. |No |

____ 2. How are the two angles related?

[pic]

|a. |vertical |c. |complementary |

|b. |supplementary |d. |adjacent |

____ 3. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?

[pic]

|a. |10 miles |c. |about 8 miles |

|b. |50 miles |d. |about 40 miles |

____ 4. Which statement is true?

[pic]

|a. |[pic]are same-side angles. |

|b. |[pic]are same-side angles. |

|c. |[pic]are alternate interior angles. |

|d. |[pic]are alternate interior angles. |

____ 5. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.

|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |

____ 6. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____.

|a. |(n – 2)180 |b. |360 |c. |[pic] |d. |180n |

____ 7. 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. |

____ 8. Based on the given information, what can you conclude, and why?

Given: [pic] [pic]

[pic]

|a. |[pic] by ASA |c. |[pic] by ASA |

|b. |[pic] by SAS |d. |[pic] by SAS |

____ 9. 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 |

____ 10. Name the smallest angle of [pic] The diagram is not to scale.

[pic]

|a. |[pic] |

|b. |[pic] |

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

|d. |[pic] |

____ 11. 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 cm |

|b. |10 cm, 15 cm, 24 cm |d. |21 cm, 7 cm, 6 cm |

____ 12. Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side?

|a. |[pic] |c. |x > 10 and x < 18 |

|b. |x > 8 and x < 28 |d. |[pic] |

____ 13. Which statement is true?

|a. |All quadrilaterals are rectangles. |

|b. |All quadrilaterals are squares. |

|c. |All rectangles are quadrilaterals. |

|d. |All quadrilaterals are parallelograms. |

____ 14. What is the missing reason in the proof?

Given: parallelogram ABCD with diagonal [pic]

Prove: [pic]

[pic]

|Statements |Reasons |

|1. [pic] |1. Definition of parallelogram |

|2. [pic] |2. Alternate Interior Angles Theorem |

|3. [pic] |3. Definition of parallelogram |

|4. [pic] |4. Alternate Interior Angles Theorem |

|5. [pic] |5. Reflexive Property of Congruence |

|6. [pic] |6. ? |

|a. |Reflexive Property of Congruence |c. |Alternate Interior Angles Theorem |

|b. |ASA |d. |SSS |

Short Answer

15. Are O, N, and P collinear? If so, name the line on which they lie.

[pic]

16. If [pic] and [pic] then what is the measure of [pic] The diagram is not to scale.

[pic]

17. Name an angle supplementary to [pic]

[pic]

18. Find the circumference of the circle in terms of π.

[pic]

19. Write this statement as a conditional in if-then form:

All triangles have three sides.

20. What is the converse of the following conditional?

If a point is in the first quadrant, then its coordinates are positive.

21. When a conditional and its converse are true, you can combine them as a true ____.

22. Name the Property of Equality that justifies the statement:

If p = q, then [pic].

23. Name the Property of Congruence that justifies the statement:

If [pic].

24. [pic]. Find the value of x for p to be parallel to q. The diagram is not to scale.

[pic]

25. Find the value of k. The diagram is not to scale.

[pic]

26. Find the values of x, y, and z. The diagram is not to scale.

[pic]

27. Find the value of the variable. The diagram is not to scale.

[pic]

28. Find the missing angle measures. The diagram is not to scale.

[pic]

29. Use the information given in the diagram. Tell why [pic] and [pic]

[pic]

30. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale.

[pic]

31. Justify the last two steps of the proof.

Given: [pic] and [pic]

Prove: [pic]

[pic]

Proof:

|1. [pic] |1. Given |

|2. [pic] |2. Given |

|3. [pic] |3. [pic] |

|4. [pic] |4. [pic] |

32. From the information in the diagram, can you prove [pic]? Explain.

[pic]

33. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?

[pic]

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

[pic]

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

[pic]

36. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.

[pic]

37. Q is equidistant from the sides of [pic] Find the value of x. The diagram is not to scale.

[pic]

38. [pic] bisects [pic] Find FG. The diagram is not to scale.

[pic]

39. Name a median for [pic]

[pic]

40. 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.

41. What is the name of the segment inside the large triangle?

[pic]

42. ABCD is a parallelogram. If [pic] then [pic] The diagram is not to scale.

[pic]

43. For the parallelogram, if [pic] and [pic] find [pic] The diagram is not to scale.

[pic]

44. In the parallelogram, [pic] and [pic] Find [pic] The diagram is not to scale.

[pic]

45. In the rhombus, [pic] Find the value of each variable. The diagram is not to scale.

[pic]

46. Find the values of a and b.The diagram is not to scale.

[pic]

47. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower?

48. If [pic] then 3a = ____.

Solve the proportion.

49. [pic]

50. Solve the extended proportion [pic] for x and y with x > 0 and y > 0.

51. An artist’s canvas forms a golden rectangle. The longer side of the canvas is 33 inches. How long is the shorter side? Round your answer to the nearest tenth of an inch.

52. Are the triangles similar? If so, explain why.

[pic]

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

53. [pic]

54. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale.

[pic]

55. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.

[pic]

56. Given: [pic]. Find the length of [pic]. The diagram is not drawn to scale.

[pic]

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

57. [pic]

58. [pic] is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale.

[pic]

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

[pic]

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)

60. [pic] 111

[pic]

Find the length of the missing side. The triangle is not drawn to scale.

61. [pic]

Find the value of x to the nearest degree.

62. [pic]

63. Write the ratios for sin A and cos A.

[pic]

64. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of [pic] to the nearest degree.

[pic]

65. The area of a square garden is 50 m2. How long is the diagonal?

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

66. Triangles ABC and DEF are similar. Find the lengths of AB and EF.

[pic]

67. Write the tangent ratios for [pic] and [pic].

[pic]

68. In triangle ABC, [pic] is a right angle and [pic] 45°. Find BC. If you answer is not an integer, leave it in simplest radical form.

[pic]

69. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.

70. If [pic] find the values of x, EF, and FG. The drawing is not to scale.

[pic]

71. Find AC.

[pic]

72. Which point is the midpoint of [pic]?

[pic]

73. [pic] bisects [pic], [pic], [pic]. Find [pic]. The diagram is not to scale.

[pic]

Find the length of the missing side. Leave your answer in simplest radical form.

74. [pic]

75. Name the ray in the figure.

[pic]

Solve for x.

76. [pic]

77. Name a fourth point in plane TUW.

[pic]

78. Find the value of x.

[pic]

79. Line r is parallel to line t. Find m[pic]5. The diagram is not to scale.

[pic]

80. In the figure, the horizontal lines are parallel and [pic] Find JM. The diagram is not to scale.

[pic]

GEOM. FINAL EXAM REVIEW PACKAGE

Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L2 REF: 1-3 Points, Lines, and Planes

OBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1

STA: MA G.G.1b TOP: 1-4 Example 1 KEY: point | collinear points | reasoning

2. ANS: B 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: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles

3. 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: MA G.G.12

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

4. 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: MA G.G.2 | MA G.G.2b TOP: 3-1 Example 1

KEY: same-side interior angles | alternate interior angles

5. ANS: D PTS: 1 DIF: L2

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

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7

KEY: Polygon Angle-Sum Theorem

6. ANS: B PTS: 1 DIF: L2

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

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7

KEY: Polygon Exterior Angle-Sum Theorem

7. ANS: C PTS: 1 DIF: L2

REF: 3-7 Slopes of Parallel and Perpendicular Lines

OBJ: 3-7.2 Slope and Perpendicular Lines

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

STA: MA G.G.6 | MA G.G.11 | MA G.G.11a | MA G.G.11b | MA G.G.11c | MA G.G.12 | MA G.G.13

KEY: slopes of perpendicular lines | perpendicular lines | reasoning

8. ANS: A PTS: 1 DIF: L2

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: MA G.G.2 | MA G.G.2b | MA G.G.6 TOP: 4-3 Example 4

KEY: ASA | reasoning

9. ANS: A PTS: 1 DIF: L3

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

NAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12

KEY: incenter of the triangle | angle bisector | reasoning

10. 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: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 2

KEY: Theorem 5-10

11. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles

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

STA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 4

KEY: Triangle Inequality Theorem

12. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles

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

STA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 5

KEY: Triangle Inequality Theorem

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

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.11 | MA G.G.11a | MA G.G.12

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

14. ANS: B PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms

OBJ: 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3f

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

KEY: proof | two-column proof | parallelogram | diagonal

SHORT ANSWER

15. ANS:

No, the three points are not collinear.

PTS: 1 DIF: L2 REF: 1-3 Points, Lines, and Planes

OBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1

STA: MA G.G.2b TOP: 1-4 Example 1 KEY: point | line | collinear points

16. ANS:

20

PTS: 1 DIF: L2 REF: 1-6 Measuring Angles

OBJ: 1-6.1 Finding Angle Measures NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g

STA: MA G.G.6 TOP: 1-6 Example 3 KEY: Angle Addition Postulate

17. ANS:

[pic]

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: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles

18. ANS:

78π in.

PTS: 1 DIF: L2 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: MA G.G.1 | MA G.G.12 | MA G.M.1 TOP: 1-9 Example 2

KEY: circle | circumference

19. ANS:

If a figure is a triangle, then it has three sides.

PTS: 1 DIF: L2 REF: 2-1 Conditional Statements

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

STA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 2

KEY: hypothesis | conclusion | conditional statement

20. ANS:

If the coordinates of a point are positive, then the point is in the first quadrant.

PTS: 1 DIF: L2 REF: 2-1 Conditional Statements

OBJ: 2-1.2 Converses NAT: NAEP 2005 G5a

STA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 5

KEY: conditional statement | coverse of a conditional

21. ANS:

biconditional

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

STA: MA G.G.2b | MA G.G.2c TOP: 2-2 Example 1

KEY: conditional statement | biconditional statement

22. ANS:

Subtraction Property

PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra

OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry

NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1

STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-4 Example 3

KEY: Properties of Equality

23. ANS:

Symmetric Property

PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra

OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry

NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1

STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-4 Example 3

KEY: Properties of Congruence

24. ANS:

20

PTS: 1 DIF: L2 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: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 3-3 Example 2

KEY: parallel lines

25. ANS:

73

PTS: 1 DIF: L2 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: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 3-4 Example 1

KEY: triangle | sum of angles of a triangle

26. ANS:

[pic]

PTS: 1 DIF: L2 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: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7

TOP: 3-4 Example 1 KEY: triangle | sum of angles of a triangle

27. ANS:

19

PTS: 1 DIF: L3 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: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7

KEY: triangle | sum of angles of a triangle | vertical angles

28. ANS:

x = 114, y = 56

PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems

OBJ: 3-5.2 Polygon Angle Sums

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7

TOP: 3-5 Example 4 KEY: exterior angle | Polygon Angle-Sum Theorem

29. ANS:

Reflexive Property, Given

PTS: 1 DIF: L2 REF: 4-1 Congruent Figures

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

STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 4

KEY: congruent figures | corresponding parts | proof

30. ANS:

3

PTS: 1 DIF: L2 REF: 4-1 Congruent Figures

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

STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 1

KEY: congruent figures | corresponding parts

31. ANS:

Reflexive Property of [pic]; SSS

PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS

OBJ: 4-2.1 Using the SSS and SAS Postulates NAT: NAEP 2005 G2e | ADP K.3

STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-2 Example 1

KEY: SSS | reflexive property | proof

32. ANS:

yes, by ASA

PTS: 1 DIF: L2 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: MA G.G.2 | MA G.G.2b | MA G.G.6 TOP: 4-3 Example 3

KEY: ASA | reasoning

33. ANS:

71°

PTS: 1 DIF: L2 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: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 | MA G.G.8

TOP: 4-5 Example 2

KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem

34. ANS:

[pic]

PTS: 1 DIF: L3 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: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 | MA G.G.8

TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem | isosceles triangle

35. ANS:

64

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: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-1 Example 1

KEY: midsegment | Triangle Midsegment Theorem

36. ANS:

75 ft

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: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.3 | MA G.G.5 | MA G.G.6

TOP: 5-1 Example 3

KEY: midsegment | Triangle Midsegment Theorem | problem solving

37. ANS:

3

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: MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-2 Example 2

KEY: angle bisector | Converse of the Angle Bisector Theorem

38. ANS:

14

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: MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-2 Example 2

KEY: angle bisector | Angle Bisector Theorem

39. ANS:

[pic]

PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes

OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b

STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4

KEY: median of a triangle

40. ANS:

circumcenter

incenter

centroid

orthocenter

PTS: 1 DIF: L3 REF: 5-3 Concurrent Lines, Medians, and Altitudes

OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b

STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12

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

41. ANS:

midsegment

PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes

OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b

STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4

KEY: altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangle

42. ANS:

115

PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

KEY: parallelogram | opposite angles | Theorem 6-2

43. ANS:

163

PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

TOP: 6-2 Example 2

KEY: algebra | parallelogram | opposite angles | consectutive angles | Theorem 6-2

44. ANS:

129

PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

KEY: parallelogram | opposite angles

45. ANS:

x = 6, y = 84, z = 10

PTS: 1 DIF: L2 REF: 6-4 Special Parallelograms

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

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

46. ANS:

[pic] [pic]

PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 | MA G.G.7

TOP: 6-5 Example 1 KEY: trapezoid | base angles | Theorem 6-15

47. ANS:

1 : 725

PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions

OBJ: 7-1.1 Using Ratios and Proportions

NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7

STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 1

KEY: ratio | word problem

48. ANS:

5b

PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions

OBJ: 7-1.1 Using Ratios and Proportions

NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7

STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 2

KEY: proportion | Cross-Product Property

49. ANS:

9

PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions

OBJ: 7-1.1 Using Ratios and Proportions

NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7

STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 3

KEY: proportion | Cross-Product Property

50. ANS:

x = 3; y = 12

PTS: 1 DIF: L4 REF: 7-1 Ratios and Proportions

OBJ: 7-1.1 Using Ratios and Proportions

NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7

STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 4

KEY: extended proportion | Cross-Product Property

51. ANS:

20.4 in.

PTS: 1 DIF: L2 REF: 7-2 Similar Polygons

OBJ: 7-2.2 Applying Similar Polygons

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

STA: MA G.G.2b | MA G.G.5 TOP: 7-2 Example 5

KEY: similar polygons

52. ANS:

yes, by AA

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: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2

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

53. ANS:

[pic]; SAS

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: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2

KEY: Side-Angle-Side Similarity Theorem | corresponding sides

54. ANS:

42.3 m

PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar

OBJ: 7-3.2 Applying AA, SAS, and SSS Similarity

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

STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 4

KEY: Side-Angle-Side Similarity Theorem | word problem

55. ANS:

[pic]

PTS: 1 DIF: L2 REF: 7-4 Similarity in Right Triangles

OBJ: 7-4.1 Using Similarity in Right Triangles

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

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5

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

56. ANS:

9

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: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 1

KEY: Side-Splitter Theorem

57. ANS:

4

PTS: 1 DIF: L2 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: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 2

KEY: side length using tangent | tangent | tangent ratio

58. ANS:

7

PTS: 1 DIF: L2 REF: 12-1 Tangent Lines

OBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4

STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 TOP: 12-1 Example 3

KEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem

59. ANS:

208 feet

PTS: 1 DIF: L2 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: MA G.G.12 TOP: 1-9 Example 1 KEY: perimeter | rectangle

60. ANS:

69

PTS: 1 DIF: L2 REF: 12-1 Tangent Lines

OBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4

STA: MA G.G.16 TOP: 12-1 Example 1

KEY: tangent to a circle | point of tangency | properties of tangents | central angle

61. ANS:

10

PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse

OBJ: 8-1.1 The Pythagorean Theorem

NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3

STA: MA G.G.2b | MA G.G.5 TOP: 8-1 Example 1

KEY: Pythagorean Theorem | leg | hypotenuse

62. ANS:

22

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: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3

KEY: inverse of tangent | tangent | tangent ratio | angle measure using tangent

63. ANS:

[pic]

PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios

OBJ: 8-4.1 Using Sine and Cosine in Triangles

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

STA: MA G.G.6 | MA G.G.9 TOP: 8-4 Example 1

KEY: sine | cosine | sine ratio | cosine ratio

64. ANS:

22[pic]

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: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3

KEY: angle measure using tangent | word problem | problem solving | tangent | inverse of tangent | tangent ratio

65. ANS:

10 m

PTS: 1 DIF: L2 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: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.7 | MA G.G.8 | MA G.G.10

TOP: 8-2 Example 3 KEY: special right triangles | diagonal

66. ANS:

AB = 10; EF = 2

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: MA G.G.2b | MA G.G.5 TOP: 7-2 Example 3

KEY: corresponding sides | proportion | similar polygons

67. ANS:

[pic]

PTS: 1 DIF: L2 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: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.7 | MA G.G.8 | MA G.G.10

TOP: 8-3 Example 1

KEY: tangent ratio | tangent | leg opposite angle | leg adjacent to angle

68. ANS:

11[pic] ft

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: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10

TOP: 8-2 Example 1 KEY: special right triangles

69. ANS:

no; [pic]

PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse

OBJ: 8-1.2 The Converse of the Pythagorean Theorem

NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10

TOP: 8-1 Example 4 KEY: Pythagorean Theorem

70. ANS:

x = 10, EF = 8, FG = 15

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: MA G.G.1b | MA G.G.12 TOP: 1-5 Example 2

KEY: segment | segment length

71. ANS:

12

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: MA G.G.1b | MA G.G.16 TOP: 1-5 Example 1

KEY: segment | segment length

72. ANS:

D

PTS: 1 DIF: L3 REF: 1-5 Measuring Segments

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

STA: MA G.G.1b | MA G.G.12 TOP: 1-5 Example 3

KEY: segment length | segment | midpoint

73. ANS:

61

PTS: 1 DIF: L3 REF: 1-7 Basic Constructions

OBJ: 1-7.2 Constructing Bisectors NAT: NAEP 2005 G3b | ADP K.2.2 | ADP K.2.3

STA: MA G.G.1b | MA G.G.4 TOP: 1-7 Example 4

KEY: angle bisector

74. ANS:

[pic] m

PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse

OBJ: 8-1.1 The Pythagorean Theorem

NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3

STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10

TOP: 8-1 Example 2 KEY: Pythagorean Theorem | leg | hypotenuse

75. ANS:

[pic]

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: MA G.G.1b TOP: 1-4 Example 1 KEY: ray

76. ANS:

[pic]

PTS: 1 DIF: L3 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: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 2

KEY: corollary of Side-Splitter Theorem

77. ANS:

Z

PTS: 1 DIF: L3 REF: 1-3 Points, Lines, and Planes

OBJ: 1-3.2 Basic Postulates of Geometry NAT: NAEP 2005 G1c | ADP K.1.1

STA: MA G.G.1b TOP: 1-4 Example 4 KEY: point | plane

78. ANS:

–19

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: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-5 Example 1

KEY: vertical angles | Vertical Angles Theorem

79. ANS:

135

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

STA: MA G.G.2 | MA G.G.2b TOP: 3-1 Example 4

KEY: parallel lines | alternate interior angles

80. ANS:

9

PTS: 1 DIF: L2 REF: 6-2 Properties of Parallelograms

OBJ: 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3f

STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6

TOP: 6-2 Example 4 KEY: transversal | parallel lines | Theorem 6-4

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