Download Geometry Name Final Exam Review Questions Spiral Review for the

Geometry
Final Exam Review Questions
Name ________________________________________
Spiral Review for the Final Exam
Order of the Chapters: 1,3,9,5,6,11,8,Composite Figures,12,10,7,2,4
Chapter 1: 1-16
1) If two lines intersect, their intersections will be exactly one ___________________________.
2) If two planes intersect, their intersection will be exactly one __________________________.
Find the intersection of the following lines and planes in the figure at the right.
3)
and
_________________
4) planes GLM and LPN _________________
5) planes GHPN and KJP ________________
7)
and plane KJN ________________
6) planes HJN and GKL ______________
8)
and plane GHL _________________
9) Use the points A(9, 2) and B(-1, 6) to find the length of AB.
10) Use the points A(3, 8) and (-2, 6) to find the length of AB.
11) Use the points A(-5, 6) and B(4, -7) to find the length of AB.
12) Use the points A(-4, -5) and B(-2, 3) to find the length of AB.
13) Use the points A(9, 2) and B(-1, 6) to find the midpoint of AB.
14) Use the points A(3, 8) and (-2, 6) to find the midpoint of AB.
15) Use the points A(-5, 6) and B(4, -7) to find the midpoint of AB.
16) Use the points A(-4, -5) and B(-2, 3) to find the midpoint of AB.
Chapter 3: 17-23
17) Find the measure of an interior angle for a regular hexagon.
18) Find the measure of an interior angle for a regular dodecagon.
19) Find the measure of an interior angle for a regular 16-gon.
20) Find the measure of an interior angle for a regular octagon.
21) Find the measure of an interior angle for a regular 18-gon.
Complete the proof.
22)
1) a || b and x || y
1) given
2) <1 + <2 = 180o
2) ______________________
3) _______________
3 _______________________
4) <1 + <3 = 180o
4 ________________________
1) a || b and x || y
1) given
2) <2 = <3
2) ___________________________
3) ____________
3) ____________________________
4) <2 = <1
4) ____________________________
23)
Chapter 9: 24-37
State whether the transformation is an isometry. Explain.
24.
25.
26.
27. Use an ordered pair for a translation 3 units left and 2 units down.
28. Describe in words the translation represented by the rule ( x, y )  ( x  6, y  4) .
29. Describe in words a translation of ( x, y )  ( x  6, y  3) followed by a translation of
.
Sketch each figure and point A.
Draw the image of each figure for the given rotation about A. Label the vertices of the image.
30.
31. Find the image of
with vertices
, and R(0, 6) for the translation
.
Judging from appearance, tell what type(s) of symmetry each figure has. If it has line symmetry, sketch the figure and
the line(s) of symmetry. If it has rotational symmetry, state the angle of rotation.
32.
33.
34.
35.
Judging from appearance, is one figure a translation image or rotation image of the other? Explain.
36.
37.
Chapter 5: 38-51
38) XY is the perpendicular bisector of AB.
Name 2 equal lengths.
39) AB is the perpendicular bisector of XY.
Name 2 equal lengths.
For Exercises 40–42, what can you conclude about each of the following from the diagram at the right? Explain.
40.
41.
and
42. the value of
Find the value of x.
43.
45. a.
44.
is the midsegment of
b.
,
.
Find MP.
. Find the perimeter of
.
Use the figure at the far right for Exercises 46–47.
46. What can
be called?
47. What can you conclude about
and
?
Can a triangle have sides with the given lengths? Explain.
48. 4 m, 8 m, 6 m
49. 2.6 ft, 4.1 ft, 6.7 ft
List the angles of each triangle in order from largest to smallest.
50.
51.
Chapter 6: 52-65
True or False.
52) All squares are rectangles.
53) A trapezoid is a parallelogram.
55) All quadrilaterals are parallelograms.
56) All squares are quadrilaterals.
54) A rhombus is a kite.
Find the values for the missing variables.
57)
58)
59)
Find the missing angles.
60)
61)
62)
63)
64) Given pints A(1, 2), B(2, 5) and C(5, 3); find point D
that will make ABCD a parallelogram.
65) Given pints A(1, 2), B(6, 0) and C(5, 3); find point D
that will make ABCD a parallelogram.
Chapter 11: 66-75
EX 1.
EX 2.
66. Find the surface area of the prism in Exercise 1.
67. Find the surface area of the cylinder in Exercise 2. Leave your answer in terms of
.
68. A truck with 18 wheels has a tire radius of 21 in. and a profile, or tire width, of 12 in. If 20% of the tire is making
contact with the ground, what is the total surface area of the tires that is making contact with the ground at any
one time? Leave your answer in terms of .
Find the surface area and volume of each figure to the nearest tenth.
69.
70.
71.
72.
73.
74.
75. Critical Thinking What is the volume of the empty space left when three tennis balls with a diameter of 3 in. are
packed into a cylindrical container that is 9 in. tall with the same diameter as the tennis balls? Round your answer to
the nearest tenth.
Chapter 8: 76-100
Find the length of the missing sides in the triangle. Write your answers in simplified radical form.
76)
77)
78)
79)
Find the values of x. Round your answer to the nearest tenth.
80)
81)
84)
82)
85)
83)
86)
87) A person looking out from the Statue of Liberty is 250ft above the ground. The angle of depression from that person to a ship on
the water is 18o. How far is the ship from the base of the statue? (Draw a picture)
88) A surveyor stands 200ft from a building to measure its height. The angle of elevation to the top of the building is 35o. How tall
is the building? (Draw a picture)
89) A hang glider is standing at the top of a cliff and sights his landing area at 23 o angle of depression. The landing area is 950ft
from the base of the cliff. How tall is the cliff? (Draw a picture)
90) An airplane pilot sights a life raft at a 26o angle of depression. The airplane’s altitude is 3 km. What is the airplane’s surface
distance from the raft? (Draw a picture)
Find the missing variables.
91)
92)
93)
94)
Composites: 95-100
Find the Surface Area and Volume of each figure.
95
96
97
98
99
100
Chapter 12: 101-117
Each polygon circumscribes a circle. Find the perimeter of the polygon.
101.
102.
103.
104.
105.
106.
107.
108.
109.A
Find the value of each variable.
Assume that lines that appear to be tangent are tangent. Find the value of each variable.
110.
111.
112.
Write an equation for each circle.
113. center (0, 1);
114. center
; through
Find the value of x.
115.
116.
117.
Chapter 10: 118-138
118) Find the area.
119) Find the area.
120) Find the area.
121) The area of a triangle is 270 in2 and the height is 12 in. Find the length of the base.
122) The area of a triangle is 142.5 cm2 and the height is 15 cm. Find the length of the base.
123) The area of a triangle is 160 in2 and the height is 10 in. Find the length of the base.
124) Name the major arc and find its measure.
125) Name the major arc and find
126) Name the major arc and find
its measure.
V
Find the length of each arc and leave your answer in terms of
127) Arc AB
128) Arc CDE

its measure.
.
129) Arc FH
Find the area of the figure to the nearest tenth.
130)
131)
132)
Find the area of each kite.
133)
134)
135)
137)
138)
Find the area of each hexagon.
136)
Chapter 7: 139-156
139) State the correct similarity statement for the given triangles.
141)
a.
d.
142) Find x.
140) State the correct similarity statement for the given triangles.
. Complete the proportions and congruence statements.
b.
e.
c.
f.
143) Find x.
144) The two shapes are similar. Which is a correct proportion for the corresponding sides?
a)
145) The two parallelograms are similar. Find x.
15 6

x 9
b)
15 x

6 9
c)
15 x

9 6
146) The two trapezoids are similar. Find x.
147) Natasha places a mirror on the ground 24ft from the base of an oak tree. She
walks backward until she can see the top of the tree in the middle of the mirror.
At that point, Natasha’s eyes are 5.5ft above the ground, and her feet are 4ft
from the image in the mirror. Find the height of the oak tree.
148) A crate is 14.5ft high and casts a 2ft shadow. At the same time, an apple tree casts an 18ft shadow.
How tall is the tree?
149) A meter stick is held perpendicular to the ground. It casts a shadow 1.5 m long. At the same time a telephone pole
casts a shadow that is 9 m long. How tall is the telephone pole?
150) A photographic negative is 3 cm by 2 cm. If a similar print from the negative is 9 cm long on its shorter side, what
is the length of its longer side?
151) Find the value of x.
154) Find the value of x and y.
152) Find the value of x.
155) Find the value of x and y.
153) Find the value of x.
156) Find the value of x and y.
Chapter 2: 157-175
157) Draw a conclusion from the two given statements.
If the measures of two angles have a sum of
, then the angles are complementary.
158) Draw a conclusion from the two given statements.
If the football team wins on Friday night, then practice is canceled for Monday.
The football team won by 7 points on Friday night.
159) Draw a conclusion from the two given statements.
If a triangle has one
In
,
angle, then the triangle is a right triangle.
.
160) Draw a conclusion from the two given statements.
If a person lives in Omaha, then he or she lives in Nebraska.
Tamika lives in Omaha.
161) True or False.
I f two angles are congruent, then they have equal measurements.
<A and <B are congruent.
Then <A = <B
162) Find x.
163) Find x.
164)
165)
166)
167)
168) Use the given conditional. If it is 12:00 noon, then the sun is shining.
a) State the converse.
b) State the truth of the converse. If false, state a counterexample.
169) Use the given conditional. If the car is full of gas, then the engine will start.
a) State the converse.
b) State the truth of the converse. If false, state a counterexample.
170) Use the given conditional. If a figure has eight sides, then it is an octagon.
a) State the converse.
b) State the truth of the converse. If false, state a counterexample.
171) Use the given conditional. If two angles have the same measure, then they are congruent.
a) State the converse.
b) State the truth of the converse. If false, state a counterexample.
172) Fill in the reason that justifies each step.
173)
174)
175)
Chapter 4: 176-188
Which theorem or postulate lets you conclude the triangles congruent. SSS, SAS, ASA, AAS
176)
177)
178)
179)
180)
181)
Write a proof for the following.
182)
Given:
Prove:
183)
Given:
Prove:
184)
Given:
Prove:
185)
Given:
Prove:
Find the values of x, y, and z.
186)
187)
188)