Download Geometry review 2

Geometry review 2
Name:
1.
Date:
There are 2 restaurants in River City located at
map points (2; 5) and (2; 9).
2.
Ben is building a new restaurant located halfway
between the existing restaurants. What is the
location of Ben's restaurant?
A.
(2; 13)
B.
C.
(2; 4)
D. (2; 1)
Aleta was completing a puzzle picture by
connecting ordered pairs of points. Her next point
is ( 4; 3).
Which point is located at ( 4; 3)?
(2; 7)
A.
page 1
Q
B.
R
C.
S
D. T
3.
Which of the following appears to be at (5; 2) on
the grid?
A.
E
B.
F
C.
G
D. H
page 2
Geometry review 2
4.
Norma will use the grid to plot the ordered pairs (3; 4), (4; 6), (7; 6), and (8; 4). If she connects the four points
with line segments, which gure will represent her drawing?
A.
B.
C.
D.
page 3
Geometry review 2
5.
6.
Which of the following best represents the
coordinates of the points shown on the grid below?
A.
( 3; 5), (0; 6), (2; 2)
B.
( 5; 3), (0; 6), (2; 2)
C.
(3; 5), ( 6; 0), ( 2; 2)
In which quadrant on the coordinate plane
would an ordered pair be graphed when the rst
coordinate is positive and the second coordinate is
negative (+; )?
A.
I
B.
II
C.
III
D. IV
D. (3; 5), (0; 6), ( 2; 2)
page 4
Geometry review 2
7.
Look at the pattern below.
8.
The two most popular tourist attractions in a city
are shown on the grid below. A hotel advertises
that it is located at the midpoint between the
tourist attractions.
If the pattern continues, which of these would be
next in the pattern?
A.
B.
C.
D.
What are the coordinates of the hotel?
page 5
(4 21 ; 5 12 )
A.
(3 21 ; 6)
B.
C.
(4 12 ; 6)
D. (6; 4 21 )
Geometry review 2
9.
Triangle JKL is shown on the grid below.
11.
Triangle JKL has vertices at (0; 0), (2; 0), and
(0; 1). How can triangle JKL be classi ed?
A.
right scalene triangle
B.
right isosceles triangle
C.
scalene triangle, but not a right triangle
D. isosceles triangle, but not a right triangle
What is the length of KL? Round the answer to
the nearest tenth of a unit.
10.
A.
3.2 units
B.
C.
11.4 units
D. 11.7 units
12.
4.0 units
Which pair of angles x and y are supplementary?
A.
mOx = 113
mOy = 67
B.
mOx = 76
mOy = 14
C.
mOx = 140
mOy = 190
D.
mOx = 180
mOy = 180
Isosceles triangle ABC is shown below. BD is the
angle bisector of OABC.
13.
!
!
In the accompanying diagram, BD ? ABC at B and
! !
BE ? BF at B. If mOFBC = 20, what is mOEBD ?
A.
20
B.
70
C.
90
D. 110
Note: The gure is not drawn to scale.
a) Prove that BD bisects AC.
page 6
Geometry review 2
14.
In the accompanying diagram, OA ? OB and
OD ? OC. If mO3 = 39, what is mO1?
17.
!
!
In the accompanying diagram, AB and CD intersect
at E, mOAEC = 5x 20, and mODEB = 2x + 10.
Find the value of x.
15.
In the accompanying diagram, O1 and O2 are
supplementary. What is mO3?
18.
!
!
In the accompanying diagram, lines AB and CD
intersect at point E. If mOCEB = 3x 14 and
mOAED = 31, nd the value of x.
16.
In the accompanying diagram, mO ABD = 72 and
!
FBE bisects OABD. Find mOABF.
19.
!
!
In the accompanying diagram, AB and CD intersect
at E. If mOAED = 2x + 11 and mOCEB = 5x 19,
nd the value of x.
page 7
Geometry review 2
20.
21.
!
In the accompanying diagram, lines JK and
!
LM intersect at N, mOJNL = 6x 74, and
mOMNK = 2x + 30. What is the value of x ?
25.
Two vertical angles are complementary. Find the
number of degrees in each angle.
26.
In two supplementary angles, the measure of one
angle is 6 more than twice the measure of the
other. The measures of these two angles are
26 and 62
B.
32 and 58
C.
58 and 122
D. 62 and 118
Two congruent angles A and B are supplementary.
Find the measure of angle A.
27.
22.
A.
Two angles are supplementary. If one of these
angles measures 50 more than the other, nd the
measure of the smaller angle.
The measures of two angles of a triangle are 70
and 55. This triangle is
A.
a right triangle
B.
a scalene triangle
C.
an obtuse triangle
D. an isosceles triangle
23.
Two angles are supplementary. If one angle
measures twice the other, nd the number of
degrees in the smaller angle.
28.
24.
Two angles are complementary. If the measure of
one angle is 20 more than the measure of the
second angle, what is the number of degrees in
the measure of the smaller angle?
page 8
If the angles of a triangle are represented by x,
3x + 20, and 6x, the triangle must be
A.
obtuse
B.
right
C.
acute
D. isosceles
Geometry review 2
29.
30.
31.
32.
If two angles of a triangle each measure 70 , the
triangle is described as
A.
right
B.
C.
obtuse
D. isosceles
33.
The measure of the vertex angle of an isosceles
triangle is 70. Find the measure of a base angle
of the triangle.
34.
If one base angle of an isosceles triangle is 55 ,
what is the number of degrees in the vertex angle?
35.
In the accompanying diagram, what is the measure
of angle x ?
36.
In the accompanying diagram of ^ ABC, AC = BC
and mOA = 70. Find the measure of the vertex
angle.
scalene
If the sum of the measures of two angles of a
triangle is equal to the measure of the third angle,
the triangle must be
A.
acute
B.
right
C.
obtuse
D. scalene
If two angles of a triangle measure 43 and 48 ,
the triangle is
A.
acute
B.
obtuse
C.
isosceles
D. right
In ^QRS, mOQ = x, mOR = 8x 40, and
mOS = 2x. Which type of triangle is ^QRS ?
A.
isosceles
B.
right
C.
acute
D. obtuse
page 9
Geometry review 2
37.
The measures of the angles of a triangle are
represented by 4x, x + 40, and 2x. Find the value
of x.
42.
The midpoint of AB is M. If the coordinates of A
are (2; 6) and the coordinates of M are (5; 1),
nd the coordinates of B.
38.
In
of
of
of
43.
Find the distance between the points (3; 2) and
(15; 3).
a circle, diameter AB is drawn. The coordinates
A are (3; 4) and the coordinates of the center
the circle are (1; 1). What are the coordinates
B?
A.
( 1; 6)
B.
(2;
3
2)
C.
(1; 6)
D. (1;
5
2)
44. What is the length of the line segment whose
endpoints are (1; 1) and (3; 3)?
A.
39.
40.
41.
p
2 5
B.
10
C.
p
4 2
p
D. 2 2
A circle has center (3; 5) and diameter AB. The
coordinates of A are ( 4; 6). What are the
coordinates of B ?
1
2 ; 4)
A.
(
C.
(10; 1)
B.
(10; 4)
45.
What is the length of the line segment whose
endpoints are ( 1; 2) and (4; 10)?
46.
If the measure of angle A is 60 , which statement
must also be true?
D. ( 3 12 ; 5 12 )
What are the coordinates of the midpoint of
the segment whose endpoints are ( 4; 6) and
( 8; 2)?
What is the midpoint of the line segment that
connects the points (1; 2) and (6; 7)?
A.
Both angle A and its supplement are obtuse
angles.
B.
Both angle A and its supplement are acute
angles.
C.
Both angle A and its complement are obtuse
angles.
D. Both angle A and its complement are acute
angles.
page 10
Geometry review 2
47.
48.
If two angles of a triangle are complementary,
then the triangle must be
A.
obtuse
B.
C.
isosceles
D. right
50.
equilateral
Given:
!
!
^DEF, EGD, EHF,
EG = EH, and GD = HF.
Prove:
O1 = O2
Given:
!
^ABC, BED, AB = CB,
and D is the midpoint of AC.
Prove:
AE = CE.
In the accompanying diagram, ^ABC and ^ADC
are isosceles triangle with AB = BC and AD = DC.
Which statement must be true?
A.
O1 = O3
B.
OB = OD
C.
^ ABC
^ADC
D. O1 = O4
51.
49.
Given:
quadrilateral ABCD, BD intersects AC at E,
and BD bisects OABC and OADC.
Prove:
AE = EC
page 11
Geometry review 2
52.
53.
Given:
ADB, AFC, BEGC, AB = AC,
DE ? BC, FG ? BC, and
BG = CE.
Prove:
BD = CF
Given:
!
RPT is a straight line, RS = RQ,
and ST = QT.
Prove:
O SPT = OQPT
54.
55.
page 12
Given:
^EAD, ABCD, AB = DC,
and OEBC = OECB.
Prove:
^EAD is an isosceles triangle.
Given:
^ABC, BD is both the median
and the altitude of AC.
Prove:
BA = BC
Geometry review 2
56.
Given:
OCDE = OCED, AD = EB
Prove:
OACD = OBCE
59.
What is the length of the hypotenuse of a right
triangle with legs of lengths 7 and 8?
A.
60.
Given:
Prove:
OH = OJ,
K is the midpoint of HJ, and IF = IG.
61.
FK = GK
62.
58.
If the length of one of the legs of a right triangle
is 10 and the length of the other leg is 24, what is
the length of the hypotenuse?
A.
13
B.
17
C.
26
B.
15
C.
p
15
D.
p
113
If the legs of a right triangle are 4 and 7, the
length of the hypotenuse is
A.
57.
9
p
3
B.
p
33
C.
p
11
D.
p
65
In the accompanying diagram of ^ABC, a right
angle is at C, AB = 8, and AC = 4.
p
4 3
A.
12
B.
C.
p
4 5
D. 4
In ^ABC, altitude AD is drawn to base BC. If
AD = 12, AB = 15, and AC = 13, what is BC ?
A.
5
B.
9
C.
14
D. 42
D. 169
page 13
Geometry review 2
63.
In the accompanying diagram, ^ABC is an
equilateral triangle with a perimeter of 30.
66.
In the accompanying diagram of right
triangle ABC, b = 40 centimeters, mOA = 60, and
mOC = 90. Find the number of centimeters in the
length of side c.
67.
In the diagram shown of right triangle BAC,
mOA = 90, mOB = 45, and AC = 8.
What is the length of altitude h of this triangle?
A.
p
5 2
B.
p
5 3
C.
p
10 2
p
D. 10 3
64. A wall is supported by a brace 10 feet long, as
shown in the diagram. If one end of the brace is
placed 6 feet from the base of the wall, how many
feet up the wall does the brace reach?
What is the length of BC ?
A.
p
8 3
B.
p
8 2
C.
p
4 2
p
D. 16 2
65.
In the accompanying diagram of right
triangle ABC, mOC = 90, mO A = 45, and AC = 1.
Find, in radical form, the length of AB.
68.
page 14
In the diagram below, ^RST is a 3-4-5 right
triangle. The altitude, h, to the hypotenuse has
been drawn. Determine the length of h.
Geometry review 2
69.
In a right triangle where one of the angles
measures 30 , what is the ratio of the length of
the side opposite the 30 angle to the length of
the side opposite the 90 angle?
A.
70.
B.
1:2
C.
1:3
In the accompanying diagram of right triangle
ABC, a right angle is at C, AB = 26, and
mOA = 27. Find the length of BC to the nearest
tenth.
73.
In the accompanying diagram of right triangle
RUN, mOU = 90, mON = 37, and RN = 21.
p
D. 1 : 3
A base angle of an isosceles triangle measures
30 , and the length of one of the legs is 12. What
is the length of the altitude drawn to the base of
the triangle?
A.
71.
p
1: 2
72.
p
6 3
B.
12
C.
6
D. 9
In right triangle BCD, BD = 12, mO C = 90, and
mODBC = 47. Find DC to the nearest tenth.
What is the length of RU, expressed to the nearest
tenth?
A.
page 15
12.6
B.
15.8
C.
16.8
D. 34.9
Geometry review 2
74.
The center pole of a tent is 8 feet long, and a side
of the tent is 12 feet long as shown in the diagram
below.
76.
If a right angle is formed where the center pole
meets the ground, what is the measure of angle A
to the nearest degree?
A.
34
B.
42
C.
48
A tree casts a 25-foot shadow on a sunny day, as
shown in the diagram below.
If the angle of elevation from the tip of the
shadow to the top of the tree is 32 , what is the
height of the tree to the nearest tenth of a foot?
D. 56
A.
75.
In the right triangle shown in the diagram below,
what is the value of x to the nearest whole
number?
A.
12
B.
14
C.
21
77.
D. 28
page 16
13.2
B.
15.6
C.
21.2
D. 40.0
Which equation shows a correct trigonometric ratio
for angle A in the right triangle below?
A.
sin A =
15
17
B.
tan A =
8
17
C.
cos A =
15
17
D. tan A =
15
8
Geometry review 2
78.
A communications company is building a 30-foot
antenna to carry cell phone transmissions. As
shown in the diagram below, a 50-foot wire from
the top of the antenna to the ground is used to
stabilize the antenna.
79.
As shown in the diagram below, a ladder 5 feet
long leans against a wall and makes an angle of
65 with the ground. Find, to the nearest tenth of
a foot, the distance from the wall to the base of
the ladder.
Find, to the nearest degree, the measure of the
angle that the wire makes with the ground.
page 17
Geometry review 2
Problem-Attic format version 4.4.218
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_
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Geometry review 2
12/19/2014
1.
Answer:
B
21.
Answer:
90
2.
Answer:
B
22.
Answer:
65
3.
Answer:
C
23.
Answer:
60
4.
Answer:
D
24.
Answer:
35
5.
Answer:
C
25.
Answer:
45
6.
Answer:
D
26.
Answer:
C
7.
Answer:
27.
Answer:
D
8.
Answer:
28.
Answer:
A
9.
Answer:
29.
Answer:
D
10.
Answer:
30.
Answer:
B
11.
Answer:
31.
Answer:
A
12.
Answer:
A
32.
Answer:
D
13.
Answer:
A
33.
Answer:
55
14.
Answer:
39
34.
Answer:
70
15.
Answer:
35
35.
Answer:
50
16.
Answer:
144
36.
Answer:
40
17.
Answer:
10
37.
Answer:
20
18.
Answer:
15
38.
Answer:
A
19.
Answer:
10
39.
Answer:
B
20.
Answer:
26
40.
Answer:
( 6; 2)
Teacher's Key
41.
Answer:
( 72 ; 29 )
63.
Answer:
B
42.
Answer:
(8; 4)
64.
Answer:
8
43.
Answer:
13
44.
Answer:
A
45.
Answer:
13
46.
Answer:
D
47.
Answer:
D
48.
Answer:
D
49.
Answer:
[proof]
50.
Answer:
[proof]
51.
Answer:
[proof]
52.
Answer:
[proof]
53.
Answer:
[proof]
54.
Answer:
[proof]
55.
Answer:
[proof]
56.
Answer:
[proof]
57.
Answer:
[proof]
58.
Answer:
C
59.
Answer:
D
60.
Answer:
D
61.
Answer:
B
62.
Answer:
C
65.
Answer:
p
2
66.
Answer:
80
67.
Answer:
B
68.
Answer:
2.4
69.
Answer:
B
70.
Answer:
C
71.
Answer:
8.8
72.
Answer:
11.8
73.
Answer:
A
74.
Answer:
B
75.
Answer:
C
76.
Answer:
B
77.
Answer:
C
78.
Answer:
37
79.
Answer:
2.1
Page 2