Download 10-4 Practice

NAME
DATE
10-4
PERIOD
Practice
Inscribed Angles
Find each measure.
1. mAB
2. m∠X
#
"
:
90°
44°
9
$
3. mJK
4. m∠Q
-
+
;
113°
26°
2
118°
1
.
,
ALGEBRA Find each measure.
5. m∠W
:
;
(2x + 2)°
7. m∠A
"
(4x - 7)°
#
3
#
8
22°
9
6. m∠Y
(2x + 11)°
%
8. m∠D
(3y + 8)°
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
(3x - 23)°
(5y - 14)°
$
ALGEBRA Find each measure.
9. m∠A
11. m∠G
"
(3x + 6)°
& (11x + 8)°
)
1
/
(6y - 4)°
10. m∠C
#
$
'
(5y - 3)°
x°
12. m∠H
( (8x + 1)°
R
13. PROBABILITY In V, point C is randomly located so that it
= 140, what is the
does not coincide with points R or S. If mRS
probability that m∠RCS = 70?
140°
C
70°
V
S
Chapter 10
26
Glencoe Geometry
NAME
DATE
10-5
PERIOD
Practice
Tangents
Determine whether each segment is tangent to the given circle. Justify your
answer.
−−−
2. QR
−−−
1. MP
20
L
M
Q
21
50
P
28
P
48
14
R
Find x. Assume that segments that appear to be tangent are tangent. Round to the
nearest tenth if necessary.
T
3.
4. T
7x - 3
S
L
x
P
15
S
5x + 1
U
10
5.
C
18
3x
T
12
B
6.
U
V
x
14
52
18
13
D
18
6
7. CLOCKS The design shown in the figure is that of a circular clock
face inscribed in a triangular base. AF and FC are equal.
a. Find AB.
10
9
8
b. Find the perimeter of the clock.
Chapter 10
D
A
32
B 2 in.
E
11 12 1
7 6 5
F
2
4
3
7.5 in.
C
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For each figure, find x. Then find the perimeter.
NAME
DATE
10-6
PERIOD
Practice
Secants, Tangents, and Angle Measures
Find each measure. Assume that any segments that appear to be tangent are
tangent.
1. m∠1
2. m∠2
3. m∠3
L 56° V
1
R
134°
N
T
M
5. mGJ
4. m∠R
6. m∠R
P
F
Q
39°
15°
G
101°
V
H
T
J
Q
59°
T
63°
9. mYAB
C
52°
D
W
Z
Y
40
A
37°
E
10. RECREATION In a game of kickball, Rickie has to kick the
= 58 and
ball through a semicircular goal to score. If mXZ
= 122, at what angle must Rickie kick the ball to
the mXY
score? Explain.
Chapter 10
Y
B
X
B
(ball)
Z
goal
Y
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Y
116°
R
8. mCE
L
62°
S
L
7. m∠Y
X
U
2
146°
105°
3
S
J
R
K
216°
DATE
10-4
PERIOD
NAME
DATE
10-4
Practice
Word Problem Practice
Inscribed Angles
Inscribed Angles
1. ARENA A circus arena is lit by five
lights equally spaced around the
perimeter.
Find each measure.
1. mAB
2. m∠X
#
What is m∠1?
:
90°
45
4. m∠Q
113°
26°
1
Hope St.
72
2
.
,
128
What is the distance between the
intersection of Upton and Hope and the
point midway between the intersections
of Upton and Cross and Cross and Hope?
2. FIELD OF VIEW The figure shows a top
view of two people in front of a very tall
rectangular wall. The wall makes a
chord of a circle that passes through
both people.
118°
1
64.5
1.5 km
(3x - 23)°
:
;
(2x + 2)°
#
8
29
22°
9
6. m∠Y
7. m∠A
"
(4x - 7)°
#
3
(2x + 11)°
%
8. m∠D
52
(3y + 8)°
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
22
(5y - 14)°
$
41
ALGEBRA Find each measure.
9. m∠A
69
11. m∠G
"
(3x + 6)°
& (11x + 8)°
73
1
)
/
(6y - 4)°
10. m∠C
21
#
$
'
(5y - 3)°
x°
12. m∠H
( (8x + 1)°
98
R
11
−
18
Chapter 10
140°
C
70°
V
S
26
Glencoe Geometry
019_036_GEOCRMCH10_890519.indd 26
A
C
Which person has more of their
horizontal field of vision blocked by the
wall?
F
Neither; the same amount of the
field of vision is blocked for both
viewers.
E
D
a. How are ∠A and ∠BCF related?
Similarly, how are ∠E and ∠DCF
related?
3. RHOMBI Paul is interested in
circumscribing a circle around a
rhombus that is not a square. He is
having great difficulty doing so. Can you
help him? Explain.
They are supplementary.
No, because it’s impossible to
do. Opposite angles of a
rhombus are congruent, and if
the rhombus is inscribed in a
circle, the measures of the
angles must add up to 180. This
would imply that all of the angles
are 90°. A rhombus with right
angles can only be a square.
Chapter 10
B
A
B
4/8/08 019_036_GEOCRMCH10_890519.indd
11:10:11 PM
27
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Glencoe Geometry
13. PROBABILITY In V, point C is randomly located so that it
= 140, what is the
does not coincide with points R or S. If mRS
probability that m∠RCS = 70?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A12
5. INSCRIBED HEXAGONS You will prove
that the sum of the measures of
alternate interior angles in an inscribed
hexagon is 360.
ALGEBRA Find each measure.
5. m∠W
Answers (Lesson 10-4)
-
.
88
3. mJK
ve
sA
;
os
9
$
Cr
44°
+
4. STREETS Three kilometers separate the
intersections of Cross and Upton and
Cross and Hope.
Upton St.
"
PERIOD
b. Show that m∠A + m∠BCD + m∠E =
360.
Lesson 10-4
Chapter 10
NAME
m∠A + m∠BCD + m∠E =
m∠A + m∠BCF + m∠DCF +
m∠E = 180 + 180 = 360
27
Glencoe Geometry
4/8/08 7:53:31 PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Chapter 10
NAME
DATE
10-5
PERIOD
NAME
DATE
10-5
Practice
Tangents
Tangents
−−−
2. QR
−−−
1. MP
L
M
Q
21
50
P
28
Word Problem Practice
1. CANALS The concrete canal in
Landtown is shaped like a “V” at the
bottom. One day, Maureen accidentally
dropped a cylindrical tube as she was
walking and it rolled to the bottom of
the dried out concrete canal. The figure
shows a cross section of the tube at the
bottom of the canal.
Determine whether each segment is tangent to the given circle. Justify your
answer.
20
PERIOD
P
48
14
4. ROLLING A wheel is rolling down an
incline. Twelve evenly spaced diameters
form spokes of the wheel.
10
11
12
9
8 7 6
5
4
3
2
1
R
2
yes; 14 + 482 = 502
2
2
V
T
4. T
7x - 3
S
L
P
S
U
10
18
x
14
52
13
D
18
6
6; 128
7; 76
7. CLOCKS The design shown in the figure is that of a circular clock
face inscribed in a triangular base. AF and FC are equal.
a. Find AB. 9.5 in.
b. Find the perimeter of the clock. 34 in.
D
10
9
8
A
B 2 in.
E
11 12 1
7 6 5
F
2
4
3
7.5 in.
C
5. DESIGN Amanda wants to make this
design of circles inside an equilateral
triangle.
in.
V
18
spoke 10
2. PACKAGING Taylor packed a sphere
inside a cubic box. He had painted the
sides of the box black before putting the
sphere inside. When the sphere was
later removed, he discovered that the
black paint had not completely dried and
there were black marks on the sides of
the sphere at the points of tangency
with the sides of the box. If the black
marks are used as the vertices of a
polygon, what kind of polygon results?
10
T
12
B
6.
U
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
3x
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A15
18.0
For each figure, find x. Then find the perimeter.
5.
When spoke 2 is vertical, which spoke
will be perpendicular to the incline?
They are equal.
15
2
Compare the lengths AV and BV.
x
5x + 1
Answers (Lesson 10-5)
Find x. Assume that segments that appear to be tangent are tangent. Round to the
nearest tenth if necessary.
3.
60°
B
A
a square
3. JEWELRY Juanita is designing a
pendant with a circular gem inscribed in
a triangle. Find the values of x, y, and z.
Then find the perimeter of the triangle.
2x + 2
80°
2.89 in.
3x - 3
34 - 2z
40°
z+4
a. What is the radius of the large circle
to the nearest hundredth of an inch?
b. What are the radii of the smaller
circles to the nearest hundredth of
an inch?
5y - 2
60°
3y + 2
0.96 in.
Glencoe Geometry
Lesson 10-5
no; 20 + 21 ≠ 28
2
5, 2, 10, 68
Chapter 10
019_036_GEOCRMC10_890519.indd 32
32
Answers
Glencoe Geometry
Chapter 10
6/2/09 019_036_GEOCRMC10_890519.indd
12:22:27 PM
33
33
Glencoe Geometry
6/2/09 12:22:30 PM
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
DATE
10-6
PERIOD
NAME
10-6
Practice
N
T
146°
79
U
2
134°
M
113
72
G
101°
F
Q
39°
15°
V
H
Q
62°
A19
29
63°
105°
X
21
52°
W
Y
128
A
37°
Z
E
B
217
Glencoe Geometry
Rickie must kick the ball at an angle less than 32
since the measure of the angle from the ground
that a tangent would make with the goal post is 32.
037_054_GEOCRMC10_890519.indd 40
115˚
D
10. RECREATION In a game of kickball, Rickie has to kick the
= 58 and
ball through a semicircular goal to score. If mXZ
= 122, at what angle must Rickie kick the ball to
the mXY
score? Explain.
Chapter 10
40˚
9. mYAB
C
Y
5. STAINED GLASS Pablo made the
stained glass window shown. He used an
inscribed square and equilateral triangle
for the design.
116°
40
Answers
X
B
(ball)
Z
goal
Y
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Y
L
longitude line
6.3
R
60
8. mCE
7. m∠Y
line of
sight
S
L
31
173.7°
horizon
T
J
59°
T
plane
line of
sight
2. RADAR Two airplanes were tracked on
radar. They followed the paths shown in
the figure.
6. m∠R
P
4. FLYING When flying at an altitude of
5 miles, the lines of sight to the horizon
looking north and south make about a
173.7° angle. How much of the longitude
line directly under the plane is visible
from 5 miles high?
65˚
50˚
125˚
55˚
80˚
What is the acute angle between their
flight paths?
3. EASELS Francisco is a
painter. He places a
circular canvas on
his A-frame easel
and carefully centers
it. The apex of the
easel is 30° and the
measure of arc BC is
22°. What is the
measure of arc AB?
10˚
B
6/2/09 037_054_GEOCRMCH10_890519.indd
12:22:57 PM
41
85˚
125˚
95˚
55˚
20˚
90˚
C
a. Label the angle measures on the
outer edge of the triangle.
A
See diagram.
b. Label all of the arcs with their degree
measure.
See diagram.
128
Chapter 10
145˚
155˚
67.5
70˚
35˚
25˚
41
Glencoe Geometry
4/8/08 7:50:20 PM
Answers (Lesson 10-6)
5. mGJ
4. m∠R
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
R
R
3
S
J
Word Problem Practice
1. TELESCOPES Vanessa looked through
her telescope at a
mountainous
landscape. The
B
figure shows
what she saw.
Based on the
view,
approximately
A
what angle does
the side of the
mountain that runs from A to B make
with the horizontal? 60
K
216°
1
PERIOD
Secants, Tangents, and Angle Measures
Secants, Tangents, and Angle Measures
Find each measure. Assume that any segments that appear to be tangent are
tangent.
1. m∠1
2. m∠2
3. m∠3
L 56° V
DATE
Lesson 10-6
Chapter 10
NAME