Chapter
10
Chapter Review
10
Vocabulary Review
Resources
circumference (p. 568)
concentric circles (p. 568)
congruent arcs (p. 569)
congruent circles (p. 566)
diameter (p. 566)
geometric probability (p. 582)
height of a parallelogram (p. 534)
height of a trapezoid (p. 540)
height of a triangle (p. 536)
adjacent arcs (p. 567)
altitude of a parallelogram (p. 534)
apothem (p. 546)
arc length (p. 569)
base of a parallelogram (p. 534)
base of a triangle (p. 536)
center of a circle (p. 566)
central angle (p. 566)
circle (p. 566)
major arc (p. 567)
minor arc (p. 567)
pi (p. 568)
radius (p. 566)
radius of a regular polygon (p. 546)
sector of a circle (p. 576)
segment of a circle (p. 577)
semicircle (p. 567)
Student Edition
Extra Skills and Word
Problems Practice, Ch. 10, p. 734
English/Spanish Glossary, p. 779
Postulates and Theorems, p. 770
Table of Symbols, p. 763
Vocabulary and Study Skills
worksheet 10F
Spanish Vocabulary and Study
Skills worksheet 10F
Interactive Textbook Audio
Glossary
Online Vocabulary Quiz
Choose the correct term to complete each sentence.
1. You can use any side as the (altitude, base) of a triangle. base
2. A (sector, segment) of a circle is a region bounded by two radii and the
intercepted arc. sector
3. A segment that contains the center of a circle and has both endpoints on the
circle is the (diameter, circumference) of a circle. diameter
PHSchool.com
For: Vocabulary quiz
Web Code: auj-1051
Chapter Review
4. In a regular polygon, the perpendicular distance from the center to a side is the
(apothem, radius) of the parallelogram. apothem
5. Two arcs of a circle with exactly one point in common are (congruent arcs,
adjacent arcs). adjacent arcs
Skills and Concepts
To find the area of a
parallelogram
To find the area of a
triangle
To find the area of a
trapezoid
To find the area of a
rhombus or a kite
To find the area of a
regular polygon
You can find the area of a rectangle, a
parallelogram, or a triangle if you know the
base, b, and height, h.The area of a rectangle or a
parallelogram is A = bh.
h
b
The area of a triangle is A = 12 bh.
The height of a trapezoid, h, is the perpendicular
distance between the bases, b1 and b2. The area of a
trapezoid is A = 12 h(b1 + b2).
Vocabulary/Study Skills
Name
h
Class
10D: Vocabulary
ELL
L3
Date
For use with Chapter Review
Study Skill: When taking notes, make your original notes as easy to read as
possible. The amount of time needed to interpret messy notes would be
better spent rereading and thinking about them.
b1
Fill in the blanks with the word(s) that best completes the sentence.
1. The function y = ax 2 + bx + c is a
The center of a regular polygon, C, is the center of
its circumscribed circle. The radius, r, is the distance
from the center to a vertex. The apothem, a, is the
perpendicular distance from the center to a side.
The area of a regular polygon with apothem a
and perimeter p is A = 12 ap.
The area of a rhombus or kite is A = 12 d1d2.
Spanish Vocabulary/Study Skills
b2
function.
2. The function Ax + By = C is written in
3. The
of its variables.
C
form.
of a monomial is the sum of the exponents
4. A
is an expression that is a number, a variable,
or a product of a number and one or more variables.
r
a
5. The fixed number in a geometric sequence is called the
ratio.
6. The length of time over which interest is calculated is the
.
p
7. When solving a system of linear equations by graphing, any point where
all the lines intersect is the
.
8. A term that has no variable is known as a
.
9. The “fold” or line that divides a parabola into two matching halves is
called the
.
d1
10. The expression b2 - 4ac is known as the
d2
11. The
horizontal change.
© Pearson Education, Inc. All rights reserved.
10-1, 10-2, and 10-3
Objectives
.
of a line is its rate of vertical change over
12. The equation 4(5 - 2 + 3) = 4(5) - 4(2) + 4(3) represents the
property.
13. A conclusion made by inductive reasoning is called a
.
14. A relation that assigns exactly one value in the range to each value in
the domain is called a
.
15. Two or more linear equations together form a
.
16. When a parabola opens upward, the y-coordinate of the vertex is a
value of the function.
Chapter 10 Chapter Review
589
17. The point at which a parabola intersects the axis of symmetry is called
the
.
40
Reading and Math Literacy Masters
Algebra 1
589
12.
Find the area of each figure. If your answer is not an integer, leave it in simplest
radical form.
n.
4i
6.
10 m2
5m
90 in.2 8.
7.
6 ft
10 in.
13.
11 ft
9 in.
11 mm
10.
11. 6.5 cm
t
m
8f
8
m
m
4m
9.
33 ft2
8c
t
8f
60⬚
6 mm
14.
10
cm
10 ft
15 mm
6.5 cm
96 ft2
117 cm2
96 "3
Sketch each regular polygon with the given radius. Then find its area. Round your
answers to the nearest tenth. 12–14. For sketches, see left.
7c
m
mm2
12. triangle; radius 4 in.
20.8 in.2
10-4 Objective
To find the perimeters
and areas of similar
figures
13. square; radius 8 mm
128 mm2
14. hexagon; radius 7 cm
127.3 cm2
If the similarity ratio of two similar figures is ba , then the ratio of their perimeters
2
is ba , and the ratio of their areas is a 2 .
b
For each pair of similar figures, find the ratio of the area of the first figure to the
area of the second.
1:4
9:4
15.
16.
17.
12
8
3
6
4:9
6
4
18. If the ratio of areas of two similar hexagons is 8 ; 25, what is the ratio of
their perimeters? 2"2 : 5
10-5 Objectives
To find the area
of a regular polygon
using trigonometry
To find the area
of a triangle using
trigonometry
You can use trigonometry to find the areas of regular polygons.
You can also use trigonometry to find the area of a triangle when you know the
lengths of two sides and the measure of the included angle.
Area of triangle = 12 ? side length ? side length ? sine of included angle
Find the area of each polygon. Round your answers to the nearest tenth.
19. regular decagon with radius 5 ft 73.5 ft2
20. regular pentagon with apothem 8 cm 232.5 cm2
21. regular hexagon with apothem 6 in. 124.7 in.2
22. regular quadrilateral with radius 2 m 8 m2
23.
24.
25.
15 cm
65⬚
15 ft
13 ft
12 m
45⬚
19 cm
100.8 cm2
590
590
Chapter 10 Chapter Review
88.4 ft2
78⬚
12 m
70.4 m2
Alternative Assessment
Name
Class
Alternative Assessment
To find the measures of
central angles and arcs
To find circumference
and arc length
To find the areas of
circles, sectors, and
segments of circles
A circle is the set of all points in a plane equidistant Semicircle
A
from one point called the center. The measure of a
minor arc is the measure of its corresponding central
angle. The measure of a major arc is 360 minus the
O
measure of its related minor arc. Adjacent arcs have
exactly one point in common.
The circumference of a circle is C = pd or
C = 2pr. The area of a circle is A = pr 2.
A sector of a circle is a region bounded by two radii
and their intercepted arc. 0
2
The area of sector APB = mAB
360 pr .
Sketch a triangular prism and a cylinder of the same height. Label both
figures, giving only the dimensions necessary to calculate the surface area
and the volume. Then find the surface area and the volume of each solid.
Radius
Central
angle
TASK 2
Explain the similarities of and the differences between pyramids and cones.
Draw a pyramid and a cone, using variables to label the dimensions. Give
formulas for the surface area and the volume of each, using the variables in
your diagrams.
Sector
of a
B
circle
A
P
A segment of a circle is the part of a circle bounded
by an arc and the segment joining its endpoints. The
area of a segment of a circle is the difference between
the areas of the related sector and the related triangle.
26. m&APD 30
1
28. mABD 330
TASK 1
B
Arc length is a fraction0
of a circle’s circumference.
0
mAB
The length of AB = 360 2pr.
Find each measure.
Chapter 10
Minor arc
Diameter
C
ACB is a
major arc.
Form C
© Pearson Education, Inc. All rights reserved.
10-6 and 10-7 Objectives
L4
Date
Segment
of a
circle
C
Form C Test
35
A
D
0
27. mAC 120
Geometry Chapter 10
60⬚
B
P
29. m&CPA 120
C
Find the length of each arc shown in red. Leave your answer in terms of π.
30.
110⬚
4 in.
22
9π
31.
in.
3 mm
π mm
120⬚
Find the area of each shaded region. Round your answer to the nearest tenth.
18.3 m2
32.
120⬚ 6 cm
8m
10-8 Objective
To use segment and area
models to find the
probabilities of events
41.0 cm2
33.
Geometric probability uses geometric figures to represent occurrences of events.
You can use a segment model or an area model. Compare the part that represents
favorable outcomes to the whole, which represents all outcomes.
A dart hits each dartboard at a random point. Find the probability that it lands in
the shaded area.
34.
35.
36.
60⬚
1
2
or 50%
3
8
or 37.5%
1
6
or about 16.7%
Chapter 10 Chapter Review
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591