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GEOM. FINAL EXAM REVIEW PACKAGE
Multiple ChoiceIdentify 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?
52°
128°
Drawing not to scale
a. vertical c. complementaryb. supplementary d. adjacent
____ 3. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside?
OceanfrontLandview
Seaside
2 4 6 8–2–4–6–8 x
2
4
6
8
–2
–4
–6
–8
y
a. 10 miles c. about 8 milesb. 50 miles d. about 40 miles
____ 4. Which statement is true?
a. are same-side angles.
b. are same-side angles.c. are alternate interior angles.d. 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. b. c. d.
____ 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. 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:
I
L
K
H
J
a. by ASA c. by ASAb. by SAS d. by SAS
____ 9. Where can the bisectors of the angles of an obtuse triangle intersect?I. inside the triangleII. on the triangleIII. outside the trianglea. I only b. III only c. I or III only d. I, II, or II
____ 10. Name the smallest angle of The diagram is not to scale.
A B
C
5 6
7
a.b.c. Two angles are the same size and smaller than the third.
d.____ 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 cmb. 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. c. x > 10 and x < 18b. x > 8 and x < 28 d.
____ 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 Prove:
D
BA
C
Statements Reasons1. 1. Definition of parallelogram2. 2. Alternate Interior Angles Theorem3. 3. Definition of parallelogram4. 4. Alternate Interior Angles Theorem5. 5. Reflexive Property of Congruence6. 6. ?
a. Reflexive Property of Congruence c. Alternate Interior Angles Theoremb. ASA d. SSS
Short Answer
15. Are O, N, and P collinear? If so, name the line on which they lie.
M
N
O
P
16. If and then what is the measure of The diagram is not to scale.
17. Name an angle supplementary to
18. Find the circumference of the circle in terms of .
39 in.
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 .
23. Name the Property of Congruence that justifies the statement:If .
24. . Find the value of x for p to be parallel to q. The diagram is not to scale.
p q
1 23 4
5 6
25. Find the value of k. The diagram is not to scale.
62°
45° k °
26. Find the values of x, y, and z. The diagram is not to scale.
38°
56°
19°
x° y°z °
27. Find the value of the variable. The diagram is not to scale.
114°
47°x°
28. Find the missing angle measures. The diagram is not to scale.
x°y°124° 65°
125°
29. Use the information given in the diagram. Tell why and A B
CD
30. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale.
d°
e°f°
b
c
g
3
45
38°
52°
31. Justify the last two steps of the proof.Given: and Prove:
R
S T
UProof:1. 1. Given2. 2. Given3. 3. 4. 4.
32. From the information in the diagram, can you prove ? Explain.
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?
38°
Drawing not to scale
2121
34. Find the value of x. The diagram is not to scale.
T U(3x – 50)° (7x)°
S
R
||
35. Find the value of x. The diagram is not to scale.
40
40
25 25
32x
36. Use the information in the diagram to determine the height of the tree. The diagram is not to scale.
150 ft
37. Q is equidistant from the sides of Find the value of x. The diagram is not to scale.
S
Q
T
R
|
||
|
30°(2x +
24)°
38. bisects Find FG. The diagram is not to scale.
D
F
E
G
))
n + 8
3n – 4
39. Name a median for
C B
A
F
D E
|
|
))
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?
42. ABCD is a parallelogram. If then The diagram is not to scale.
A B
D C
43. For the parallelogram, if and find The diagram is not to scale.
3 4
2 1
44. In the parallelogram, and Find The diagram is not to scale.J
LM
K
O
45. In the rhombus, Find the value of each variable. The diagram is not to scale.
12
3
||
||
46. Find the values of a and b.The diagram is not to scale.
36° b°
113°a°
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 then 3a = ____.
Solve the proportion.
49.
50. Solve the extended proportion 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.
84.6° 84.6°
30.4°
65°
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
53.
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.
55. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
5 26
56. Given: . Find the length of . The diagram is not drawn to scale.
B
A
C
P Q6
12 18
Find the value of x. Round your answer to the nearest tenth.
57.x
7
Not drawn to scale
58. 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.
B
O
A
r
59. Find the perimeter of the rectangle. The drawing is not to scale.
47 ft
57 ft
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. 111
O x°
Find the length of the missing side. The triangle is not drawn to scale.
61. 6
8
Find the value of x to the nearest degree.
62.x
3
58
63. Write the ratios for sin A and cos A.
C B
A
4
3
5
Not drawn to scale
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 to the nearest degree.
A249 ft
100 ft
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.A
B C
D
FE
4
55x
x
67. Write the tangent ratios for and .
R Q
P
21
20
29
Not drawn to scale
68. In triangle ABC, is a right angle and 45. Find BC. If you answer is not an integer, leave it in simplest radical form.
AB
C
11 ft
Not drawn to scale
69. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.
70. If find the values of x, EF, and FG. The drawing is not to scale.
E GF
71. Find AC.
0 1 2 3 4 5 6 7 8 9 100–1–2–3–4–5–6–7–8–9–10
A B C D
72. Which point is the midpoint of ?
0 1 2 3 4 5 6 7 80–1–2–3–4–5–6–7–8
A EDB C
73. bisects , , . Find . The diagram is not to scale.
Find the length of the missing side. Leave your answer in simplest radical form.
74.
7 m
8 m
Not drawn to scale
75. Name the ray in the figure.A B
Solve for x.
76.3x 3x + 7
5x – 84x>
>
>
77. Name a fourth point in plane TUW.
78. Find the value of x.
(7x – 8)°
(6x + 11)°
Drawing not to scale
79. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r
t
71 3
265
4
135°
80. In the figure, the horizontal lines are parallel and Find JM. The diagram is not to scale.
3
M A
L B
K C
J D
GEOM. FINAL EXAM REVIEW PACKAGEAnswer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: L2 REF: 1-3 Points, Lines, and PlanesOBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1STA: 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 AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles
3. ANS: D PTS: 1 DIF: L3 REF: 1-8 The Coordinate PlaneOBJ: 1-8.1 Finding Distance on the Coordinate PlaneNAT: NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3 STA: MA G.G.12KEY: coordinate plane | Distance Formula | word problem | problem solving
4. ANS: D PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.1 Identifying Angles NAT: NAEP 2005 M1f | ADP K.2.1STA: MA G.G.2 | MA G.G.2b TOP: 3-1 Example 1KEY: same-side interior angles | alternate interior angles
5. ANS: D PTS: 1 DIF: L2REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7KEY: Polygon Angle-Sum Theorem
6. ANS: B PTS: 1 DIF: L2REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7KEY: Polygon Exterior Angle-Sum Theorem
7. ANS: C PTS: 1 DIF: L2REF: 3-7 Slopes of Parallel and Perpendicular LinesOBJ: 3-7.2 Slope and Perpendicular LinesNAT: NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2STA: 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.13KEY: slopes of perpendicular lines | perpendicular lines | reasoning
8. ANS: A PTS: 1 DIF: L2REF: 4-3 Triangle Congruence by ASA and AASOBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.6 TOP: 4-3 Example 4KEY: ASA | reasoning
9. ANS: A PTS: 1 DIF: L3REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.1 Properties of BisectorsNAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12KEY: incenter of the triangle | angle bisector | reasoning
10. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.1 Inequalities Involving Angles of Triangles NAT: NAEP 2005 G3fSTA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 2KEY: Theorem 5-10
11. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3fSTA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 4KEY: Triangle Inequality Theorem
12. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in TrianglesOBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3fSTA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 5KEY: Triangle Inequality Theorem
13. ANS: C PTS: 1 DIF: L2 REF: 6-1 Classifying QuadrilateralsOBJ: 6-1.1 Classifying Special Quadrilaterals NAT: NAEP 2005 G3fSTA: 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.12KEY: reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals
14. ANS: B PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6KEY: 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 PlanesOBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1STA: 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 AnglesOBJ: 1-6.1 Finding Angle Measures NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: MA G.G.6 TOP: 1-6 Example 3 KEY: Angle Addition Postulate
17. ANS:
PTS: 1 DIF: L2 REF: 1-6 Measuring AnglesOBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3gSTA: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles
18. ANS:78 in.
PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and AreaOBJ: 1-9.1 Finding Perimeter and CircumferenceNAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: MA G.G.1 | MA G.G.12 | MA G.M.1 TOP: 1-9 Example 2KEY: circle | circumference
19. ANS:If a figure is a triangle, then it has three sides.
PTS: 1 DIF: L2 REF: 2-1 Conditional StatementsOBJ: 2-1.1 Conditional Statements NAT: NAEP 2005 G5aSTA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 2KEY: 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 StatementsOBJ: 2-1.2 Converses NAT: NAEP 2005 G5aSTA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 5KEY: conditional statement | coverse of a conditional
21. ANS:biconditional
PTS: 1 DIF: L2 REF: 2-2 Biconditionals and DefinitionsOBJ: 2-2.1 Writing Biconditionals NAT: NAEP 2005 G1c | NAEP 2005 G5a | ADP K.1.1STA: MA G.G.2b | MA G.G.2c TOP: 2-2 Example 1KEY: conditional statement | biconditional statement
22. ANS:Subtraction Property
PTS: 1 DIF: L2 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and GeometryNAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-4 Example 3KEY: Properties of Equality
23. ANS:Symmetric Property
PTS: 1 DIF: L2 REF: 2-4 Reasoning in AlgebraOBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry
NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-4 Example 3KEY: Properties of Congruence
24. ANS:20
PTS: 1 DIF: L2 REF: 3-3 Parallel and Perpendicular LinesOBJ: 3-3.1 Relating Parallel and Perpendicular LinesNAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 3-3 Example 2KEY: parallel lines
25. ANS:73
PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum TheoremOBJ: 3-4.1 Finding Angle Measures in TrianglesNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 3-4 Example 1KEY: triangle | sum of angles of a triangle
26. ANS:
PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum TheoremOBJ: 3-4.1 Finding Angle Measures in TrianglesNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7TOP: 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 TheoremOBJ: 3-4.1 Finding Angle Measures in TrianglesNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7KEY: 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 TheoremsOBJ: 3-5.2 Polygon Angle SumsNAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7TOP: 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.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 4KEY: congruent figures | corresponding parts | proof
30. ANS:3
PTS: 1 DIF: L2 REF: 4-1 Congruent FiguresOBJ: 4-1.1 Congruent Figures NAT: NAEP 2005 G2e | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 1KEY: congruent figures | corresponding parts
31. ANS:Reflexive Property of ; SSS
PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SASOBJ: 4-2.1 Using the SSS and SAS Postulates NAT: NAEP 2005 G2e | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-2 Example 1KEY: SSS | reflexive property | proof
32. ANS:yes, by ASA
PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AASOBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.6 TOP: 4-3 Example 3KEY: ASA | reasoning
33. ANS:71°
PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 The Isosceles Triangle TheoremsNAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3STA: 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.8TOP: 4-5 Example 2KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
34. ANS:
PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral TrianglesOBJ: 4-5.1 The Isosceles Triangle TheoremsNAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3STA: 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.8TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem | isosceles triangle
35. ANS:64
PTS: 1 DIF: L2 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-1 Example 1KEY: midsegment | Triangle Midsegment Theorem
36. ANS:75 ft
PTS: 1 DIF: L2 REF: 5-1 Midsegments of TrianglesOBJ: 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP K.1.2STA: 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.6TOP: 5-1 Example 3KEY: midsegment | Triangle Midsegment Theorem | problem solving
37. ANS:3
PTS: 1 DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2STA: MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-2 Example 2KEY: angle bisector | Converse of the Angle Bisector Theorem
38. ANS:14
PTS: 1 DIF: L2 REF: 5-2 Bisectors in TrianglesOBJ: 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP K.2.2STA: MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 5-2 Example 2KEY: angle bisector | Angle Bisector Theorem
39. ANS:
PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and AltitudesOBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3bSTA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4KEY: median of a triangle
40. ANS:circumcenterincentercentroidorthocenter
PTS: 1 DIF: L3 REF: 5-3 Concurrent Lines, Medians, and AltitudesOBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3bSTA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12KEY: 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 AltitudesOBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3bSTA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4KEY: 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 ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6KEY: parallelogram | opposite angles | Theorem 6-2
43. ANS:163
PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6TOP: 6-2 Example 2KEY: algebra | parallelogram | opposite angles | consectutive angles | Theorem 6-2
44. ANS:129
PTS: 1 DIF: L3 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6KEY: parallelogram | opposite angles
45. ANS:x = 6, y = 84, z = 10
PTS: 1 DIF: L2 REF: 6-4 Special ParallelogramsOBJ: 6-4.1 Diagonals of Rhombuses and Rectangles NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6TOP: 6-4 Example 1 KEY: algebra | diagonal | rhombus | Theorem 6-13
46. ANS:
PTS: 1 DIF: L2 REF: 6-5 Trapezoids and KitesOBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3fSTA: 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.7TOP: 6-5 Example 1 KEY: trapezoid | base angles | Theorem 6-15
47. ANS:1 : 725
PTS: 1 DIF: L2 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 1
KEY: ratio | word problem48. ANS:
5b
PTS: 1 DIF: L2 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 2KEY: proportion | Cross-Product Property
49. ANS:9
PTS: 1 DIF: L2 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 3KEY: proportion | Cross-Product Property
50. ANS:x = 3; y = 12
PTS: 1 DIF: L4 REF: 7-1 Ratios and ProportionsOBJ: 7-1.1 Using Ratios and ProportionsNAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 4KEY: extended proportion | Cross-Product Property
51. ANS:20.4 in.
PTS: 1 DIF: L2 REF: 7-2 Similar PolygonsOBJ: 7-2.2 Applying Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.G.5 TOP: 7-2 Example 5KEY: similar polygons
52. ANS:yes, by AA
PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem
53. ANS:; SAS
PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.1 The AA Postulate and the SAS and SSS TheoremsNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2KEY: Side-Angle-Side Similarity Theorem | corresponding sides
54. ANS:42.3 m
PTS: 1 DIF: L2 REF: 7-3 Proving Triangles SimilarOBJ: 7-3.2 Applying AA, SAS, and SSS SimilarityNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 4KEY: Side-Angle-Side Similarity Theorem | word problem
55. ANS:130
PTS: 1 DIF: L2 REF: 7-4 Similarity in Right TrianglesOBJ: 7-4.1 Using Similarity in Right TrianglesNAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5TOP: 7-4 Example 2 KEY: corollaries of the geometric mean | proportion
56. ANS:9
PTS: 1 DIF: L2 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 1KEY: Side-Splitter Theorem
57. ANS:4
PTS: 1 DIF: L2 REF: 8-3 The Tangent RatioOBJ: 8-3.1 Using Tangents in TrianglesNAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2STA: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 2KEY: side length using tangent | tangent | tangent ratio
58. ANS:7
PTS: 1 DIF: L2 REF: 12-1 Tangent LinesOBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 TOP: 12-1 Example 3KEY: 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 AreaOBJ: 1-9.1 Finding Perimeter and CircumferenceNAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2STA: MA G.G.12 TOP: 1-9 Example 1 KEY: perimeter | rectangle
60. ANS:69
PTS: 1 DIF: L2 REF: 12-1 Tangent LinesOBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4STA: MA G.G.16 TOP: 12-1 Example 1KEY: 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 ConverseOBJ: 8-1.1 The Pythagorean TheoremNAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3STA: MA G.G.2b | MA G.G.5 TOP: 8-1 Example 1KEY: Pythagorean Theorem | leg | hypotenuse
62. ANS:22
PTS: 1 DIF: L3 REF: 8-3 The Tangent RatioOBJ: 8-3.1 Using Tangents in TrianglesNAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2STA: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3KEY: inverse of tangent | tangent | tangent ratio | angle measure using tangent
63. ANS:
PTS: 1 DIF: L2 REF: 8-4 Sine and Cosine RatiosOBJ: 8-4.1 Using Sine and Cosine in TrianglesNAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2STA: MA G.G.6 | MA G.G.9 TOP: 8-4 Example 1KEY: sine | cosine | sine ratio | cosine ratio
64. ANS:22
PTS: 1 DIF: L3 REF: 8-3 The Tangent RatioOBJ: 8-3.1 Using Tangents in TrianglesNAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2STA: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3KEY: 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 TrianglesOBJ: 8-2.1 45°-45°-90° Triangles NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5STA: 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.10TOP: 8-2 Example 3 KEY: special right triangles | diagonal
66. ANS:
AB = 10; EF = 2
PTS: 1 DIF: L2 REF: 7-2 Similar PolygonsOBJ: 7-2.1 Similar PolygonsNAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7STA: MA G.G.2b | MA G.G.5 TOP: 7-2 Example 3KEY: corresponding sides | proportion | similar polygons
67. ANS:
PTS: 1 DIF: L2 REF: 8-3 The Tangent RatioOBJ: 8-3.1 Using Tangents in TrianglesNAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2STA: 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.10TOP: 8-3 Example 1KEY: tangent ratio | tangent | leg opposite angle | leg adjacent to angle
68. ANS:11 ft
PTS: 1 DIF: L3 REF: 8-2 Special Right TrianglesOBJ: 8-2.1 45°-45°-90° Triangles NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10TOP: 8-2 Example 1 KEY: special right triangles
69. ANS:no;
PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.2 The Converse of the Pythagorean TheoremNAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10TOP: 8-1 Example 4 KEY: Pythagorean Theorem
70. ANS:x = 10, EF = 8, FG = 15
PTS: 1 DIF: L2 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1STA: MA G.G.1b | MA G.G.12 TOP: 1-5 Example 2KEY: segment | segment length
71. ANS:12
PTS: 1 DIF: L2 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1STA: MA G.G.1b | MA G.G.16 TOP: 1-5 Example 1KEY: segment | segment length
72. ANS:D
PTS: 1 DIF: L3 REF: 1-5 Measuring SegmentsOBJ: 1-5.1 Finding Segment Lengths NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP I.2.1STA: MA G.G.1b | MA G.G.12 TOP: 1-5 Example 3KEY: segment length | segment | midpoint
73. ANS:61
PTS: 1 DIF: L3 REF: 1-7 Basic ConstructionsOBJ: 1-7.2 Constructing Bisectors NAT: NAEP 2005 G3b | ADP K.2.2 | ADP K.2.3STA: MA G.G.1b | MA G.G.4 TOP: 1-7 Example 4KEY: angle bisector
74. ANS:113 m
PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its ConverseOBJ: 8-1.1 The Pythagorean TheoremNAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10TOP: 8-1 Example 2 KEY: Pythagorean Theorem | leg | hypotenuse
75. ANS:
PTS: 1 DIF: L2 REF: 1-4 Segments, Rays, Parallel Lines and PlanesOBJ: 1-4.1 Identifying Segments and Rays NAT: NAEP 2005 G3gSTA: MA G.G.1b TOP: 1-4 Example 1 KEY: ray
76. ANS:
PTS: 1 DIF: L3 REF: 7-5 Proportions in TrianglesOBJ: 7-5.1 Using the Side-Splitter TheoremNAT: NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 2KEY: corollary of Side-Splitter Theorem
77. ANS:Z
PTS: 1 DIF: L3 REF: 1-3 Points, Lines, and PlanesOBJ: 1-3.2 Basic Postulates of Geometry NAT: NAEP 2005 G1c | ADP K.1.1STA: MA G.G.1b TOP: 1-4 Example 4 KEY: point | plane
78. ANS:–19
PTS: 1 DIF: L2 REF: 2-5 Proving Angles CongruentOBJ: 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-5 Example 1KEY: vertical angles | Vertical Angles Theorem
79. ANS:135
PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel LinesOBJ: 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1STA: MA G.G.2 | MA G.G.2b TOP: 3-1 Example 4KEY: parallel lines | alternate interior angles
80. ANS:9
PTS: 1 DIF: L2 REF: 6-2 Properties of ParallelogramsOBJ: 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3fSTA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6TOP: 6-2 Example 4 KEY: transversal | parallel lines | Theorem 6-4
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