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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
2. How are the two angles related?
c. No
52°
128°
Drawing not to scale
____
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?
y
8
6
Seaside
4
2
–8 –6 –4 –2
–2
Landview
–4
2
4
6
8
x
Oceanfront
–6
–8
____
a. 10 miles
b. 50 miles
4. Which statement is true?
a.
are same-side angles.
c. about 8 miles
d. about 40 miles
____
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
K
J
H
L
a.
by ASA
c.
by ASA
b.
by SAS
d.
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
The diagram is not to scale.
C
5
A
6
7
B
a.
b.
c. Two angles are the same size and smaller than the third.
____ 11.
____ 12.
____ 13.
____ 14.
d.
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
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 < 18
b. x > 8 and x < 28
d.
Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
What is the missing reason in the proof?
Given: parallelogram ABCD with diagonal
Prove:
A
D
B
C
Statements
1.
2.
3.
4.
5.
6.
a. Reflexive Property of Congruence
b. ASA
Reasons
1. Definition of parallelogram
2. Alternate Interior Angles Theorem
3. Definition of parallelogram
4. Alternate Interior Angles Theorem
5. Reflexive Property of Congruence
6. ?
c. Alternate Interior Angles Theorem
d. SSS
Short Answer
15. Are O, N, and P collinear? If so, name the line on which they lie.
O
N
P
M
16. If
scale.
and
then what is the measure of
The diagram is not to
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.
3 4
5
1 2
6
p
q
25. Find the value of k. The diagram is not to scale.
62°
k°
45°
26. Find the values of x, y, and z. The diagram is not to scale.
38°
19°
56°
x°
z°
y°
27. Find the value of the variable. The diagram is not to scale.
114°
x°
47°
28. Find the missing angle measures. The diagram is not to scale.
125°
x°
124° y°
65°
29. Use the information given in the diagram. Tell why
A
and
B
D
C
30. The two triangles are congruent as suggested by their appearance. Find the value of c. The
diagrams are not to scale.
d°
38°
g
5
b
f°
e°
52°
3
c
31. Justify the last two steps of the proof.
Given:
and
Prove:
R
S
T
U
Proof:
1.
2.
3.
4.
4
1. Given
2. Given
3.
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°
21
21
Drawing not to scale
34. Find the value of x. The diagram is not to scale.
|
|
S
(3 x – 50)°
R
(7 x )°
T
U
35. Find the value of x. The diagram is not to scale.
40
x
40
32
25
25
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.
T
|
|
|
4)°
2
+
x
(2
30°
|
Q
R
S
38.
bisects
Find FG. The diagram is not to scale.
E
n +8
F
)
3n – 4
)
D
G
39. Name a median for
|
A
E
)
|
D
)
C
F B
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
scale.
and
3
find
The diagram is not to
4
2
1
44. In the parallelogram,
and
J
Find
The diagram is not to scale.
K
O
M
L
|
|
45. In the rhombus,
The diagram is not to scale.
3
1
|
|
2
46. Find the values of a and b.The diagram is not to scale.
Find the value of each variable.
a°
113°
36°
b°
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.
30.4°
84.6°
84.6°
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.
A
6
P
Q
12
18
B
C
Find the value of x. Round your answer to the nearest tenth.
57.
7

x
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
A
r
O
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
x°
O
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.
58
3
x
63. Write the ratios for sin A and cos A.
A
5
4
C
B
3
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.
100 ft
A
249 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
D
5x
5
E
B
4
x F
C
67. Write the tangent ratios for
and
.
P
29
21
R
Q
20
Not drawn to scale
68. In triangle ABC,
is a right angle and
leave it in simplest radical form.
45. Find BC. If you answer is not an integer,
C
11 ft
B
A
Not drawn to scale
69. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.
70. If
to scale.
find the values of x, EF, and FG. The drawing is not
E
F
G
71. Find AC.
A
B
C
D
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
72. Which point is the midpoint of
A
B
C
–8 –7 –6 –5 –4 –3 –2 –1
73.
bisects
not to scale.
,
?
D
0
1
E
2
3
4
5
6
7
,
8
. Find
. The diagram is
Find the length of the missing side. Leave your answer in simplest radical form.
74.
8m
7m
Not drawn to scale
75. Name the ray in the figure.
A
B
Solve for x.
76.
>
3x
4x
3x + 7
>
>
5x – 8
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
7
135°
1
3
t
4
2
5
6
80. In the figure, the horizontal lines are parallel and
scale.
M
A
3
L
K
J
B
C
D
Find JM. The diagram is not to
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:
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:
78 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
KEY: Properties of Congruence
24. ANS:
20
PTS:
OBJ:
NAT:
STA:
KEY:
25. ANS:
73
TOP: 2-4 Example 3
1
DIF: L2
REF: 3-3 Parallel and Perpendicular Lines
3-3.1 Relating Parallel and Perpendicular Lines
NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1
MA G.G.2 | MA G.G.2b | MA G.G.5
TOP: 3-3 Example 2
parallel lines
PTS: 1
DIF: L2
REF: 3-4 Parallel Lines and the Triangle AngleSum 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:
PTS: 1
DIF: L2
REF: 3-4 Parallel Lines and the Triangle AngleSum 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 AngleSum 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 ; 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:
OBJ:
K.3
STA:
KEY:
33. ANS:
71°
1
DIF: L2
REF: 4-3 Triangle Congruence by ASA and AAS
4-3.1 Using the ASA Postulate and the AAS Theorem
NAT: NAEP 2005 G2e | ADP
MA G.G.2 | MA G.G.2b | MA G.G.6
ASA | reasoning
TOP: 4-3 Example 3
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:
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:
OBJ:
K.1.2
STA:
KEY:
36. ANS:
75 ft
1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
NAT: NAEP 2005 G3f | ADP
PTS:
OBJ:
K.1.2
STA:
TOP:
KEY:
37. ANS:
3
1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Using Properties of Midsegments
NAT: NAEP 2005 G3f | ADP
PTS:
OBJ:
K.2.2
STA:
KEY:
38. ANS:
14
1
DIF: L2
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
NAT: NAEP 2005 G3b | ADP
PTS:
OBJ:
K.2.2
STA:
KEY:
39. ANS:
1
DIF: L2
REF: 5-2 Bisectors in Triangles
5-2.1 Perpendicular Bisectors and Angle Bisectors
NAT: NAEP 2005 G3b | ADP
MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
midsegment | Triangle Midsegment Theorem
TOP: 5-1 Example 1
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
5-1 Example 3
midsegment | Triangle Midsegment Theorem | problem solving
MA G.G.2b | MA G.G.5 | MA G.G.6
angle bisector | Converse of the Angle Bisector Theorem
MA G.G.2b | MA G.G.5 | MA G.G.6
angle bisector | Angle Bisector Theorem
TOP: 5-2 Example 2
TOP: 5-2 Example 2
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:
OBJ:
STA:
KEY:
43. ANS:
163
1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f
MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
parallelogram | opposite angles | Theorem 6-2
PTS:
OBJ:
STA:
TOP:
KEY:
44. ANS:
129
1
DIF: L3
REF: 6-2 Properties of Parallelograms
6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f
MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
6-2 Example 2
algebra | parallelogram | opposite angles | consectutive angles | Theorem 6-2
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:
OBJ:
STA:
TOP:
46. ANS:
1
DIF: L2
REF: 6-4 Special Parallelograms
6-4.1 Diagonals of Rhombuses and Rectangles
NAT: NAEP 2005 G3f
MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
6-4 Example 1
KEY: algebra | diagonal | rhombus | Theorem 6-13
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:
OBJ:
NAT:
STA:
1
DIF: L2
REF: 7-1 Ratios and Proportions
7-1.1 Using Ratios and Proportions
NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7
MA G.G.2b | MA G.M.5
TOP: 7-1 Example 1
KEY: ratio | word problem
48. ANS:
5b
PTS:
OBJ:
NAT:
STA:
KEY:
49. ANS:
9
1
DIF: L2
REF: 7-1 Ratios and Proportions
7-1.1 Using Ratios and Proportions
NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7
MA G.G.2b | MA G.M.5
TOP: 7-1 Example 2
proportion | Cross-Product Property
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:
; SAS
PTS:
OBJ:
NAT:
STA:
KEY:
1
DIF: L2
REF: 7-3 Proving Triangles Similar
7-3.1 The AA Postulate and the SAS and SSS Theorems
NAEP 2005 G2e | ADP I.1.2 | ADP K.3
MA G.G.2 | MA G.G.2b | MA G.G.5
TOP: 7-3 Example 2
Side-Angle-Side Similarity Theorem | corresponding sides
54. ANS:
42.3 m
PTS:
OBJ:
NAT:
STA:
KEY:
55. ANS:
130
1
DIF: L2
REF: 7-3 Proving Triangles Similar
7-3.2 Applying AA, SAS, and SSS Similarity
NAEP 2005 G2e | ADP I.1.2 | ADP K.3
MA G.G.2 | MA G.G.2b | MA G.G.5
TOP: 7-3 Example 4
Side-Angle-Side Similarity Theorem | word problem
PTS:
OBJ:
NAT:
STA:
TOP:
56. ANS:
9
1
DIF: L2
REF: 7-4 Similarity in Right Triangles
7-4.1 Using Similarity in Right Triangles
NAEP 2005 G2e | ADP I.1.2 | ADP K.3
MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5
7-4 Example 2
KEY: corollaries of the geometric mean | proportion
PTS:
OBJ:
NAT:
STA:
KEY:
57. ANS:
4
1
DIF: L2
REF: 7-5 Proportions in Triangles
7-5.1 Using the Side-Splitter Theorem
NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3
MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
TOP: 7-5 Example 1
Side-Splitter Theorem
PTS:
OBJ:
NAT:
STA:
KEY:
58. ANS:
7
1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles
NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
MA G.G.6 | MA G.G.9
TOP: 8-3 Example 2
side length using tangent | tangent | tangent ratio
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:
OBJ:
NAT:
STA:
60. ANS:
69
1
DIF: L2
REF: 1-9 Perimeter, Circumference, and Area
1-9.1 Finding Perimeter and Circumference
NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2
MA G.G.12 TOP: 1-9 Example 1
KEY: perimeter | rectangle
PTS:
OBJ:
K.4
STA:
KEY:
61. ANS:
10
1
DIF: L2
REF: 12-1 Tangent Lines
12-1.1 Using the Radius-Tangent Relationship
NAT: NAEP 2005 G3e | ADP
MA G.G.16 TOP: 12-1 Example 1
tangent to a circle | point of tangency | properties of tangents | central angle
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:
OBJ:
NAT:
STA:
KEY:
63. ANS:
1
DIF: L3
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles
NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
MA G.G.6 | MA G.G.9
TOP: 8-3 Example 3
inverse of tangent | tangent | tangent ratio | angle measure using tangent
PTS:
OBJ:
NAT:
STA:
KEY:
64. ANS:
22
1
DIF: L2
REF: 8-4 Sine and Cosine Ratios
8-4.1 Using Sine and Cosine in Triangles
NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
MA G.G.6 | MA G.G.9
TOP: 8-4 Example 1
sine | cosine | sine ratio | cosine ratio
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:
OBJ:
NAT:
STA:
KEY:
67. ANS:
1
DIF: L2
REF: 7-2 Similar Polygons
7-2.1 Similar Polygons
NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7
MA G.G.2b | MA G.G.5
TOP: 7-2 Example 3
corresponding sides | proportion | similar polygons
PTS:
OBJ:
NAT:
STA:
TOP:
KEY:
68. ANS:
11
1
DIF: L2
REF: 8-3 The Tangent Ratio
8-3.1 Using Tangents in Triangles
NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2
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
8-3 Example 1
tangent ratio | tangent | leg opposite angle | leg adjacent to angle
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;
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:
OBJ:
I.2.1
STA:
KEY:
71. ANS:
12
1
DIF: L2
1-5.1 Finding Segment Lengths
REF: 1-5 Measuring Segments
NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP
MA G.G.1b | MA G.G.12
segment | segment length
TOP: 1-5 Example 2
PTS: 1
DIF: L2
OBJ: 1-5.1 Finding Segment Lengths
I.2.1
STA: MA G.G.1b | MA G.G.16
REF: 1-5 Measuring Segments
NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP
TOP: 1-5 Example 1
KEY: segment | segment length
72. ANS:
D
PTS:
OBJ:
I.2.1
STA:
KEY:
73. ANS:
61
1
DIF: L3
1-5.1 Finding Segment Lengths
PTS:
OBJ:
STA:
KEY:
74. ANS:
113
1
DIF: L3
1-7.2 Constructing Bisectors
MA G.G.1b | MA G.G.4
angle bisector
REF: 1-5 Measuring Segments
NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP
MA G.G.1b | MA G.G.12
TOP: 1-5 Example 3
segment length | segment | midpoint
REF: 1-7 Basic Constructions
NAT: NAEP 2005 G3b | ADP K.2.2 | ADP K.2.3
TOP: 1-7 Example 4
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:
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:
PTS:
OBJ:
NAT:
STA:
KEY:
77. ANS:
Z
1
DIF: L3
REF: 7-5 Proportions in Triangles
7-5.1 Using the Side-Splitter Theorem
NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3
MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
TOP: 7-5 Example 2
corollary of Side-Splitter Theorem
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:
OBJ:
STA:
KEY:
79. ANS:
135
1
DIF: L2
REF: 2-5 Proving Angles Congruent
2-5.1 Theorems About Angles
NAT: NAEP 2005 G3g | ADP K.1.1
MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6
TOP: 2-5 Example 1
vertical angles | Vertical Angles Theorem
PTS:
OBJ:
STA:
KEY:
80. ANS:
9
1
DIF: L2
REF: 3-1 Properties of Parallel Lines
3-1.2 Properties of Parallel Lines
NAT: NAEP 2005 M1f | ADP K.2.1
MA G.G.2 | MA G.G.2b
TOP: 3-1 Example 4
parallel lines | alternate interior angles
PTS:
OBJ:
STA:
TOP:
1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.2 Properties: Diagonals and Transversals
NAT: NAEP 2005 G3f
MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6
6-2 Example 4
KEY: transversal | parallel lines | Theorem 6-4