GEOM
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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