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Polygons
Word Watch
quadrilateral, p. 494
trapezoid, p. 494
parallelogram, p. 494
rhombus, p. 494
polygon, p. 495
pentagon, p. 495
hexagon, p. 495
heptagon, p. 495
octagon, p. 495
regular polygon, p. 496
BEFORE
Now
WHY?
You classified triangles.
You’ll classify quadrilaterals
and other polygons.
So you can classify the polygons in
a stained glass window, as in Ex. 15.
A quadrilateral is a geometric figure that is made up of four line
segments, called sides, that intersect only at their endpoints. Some
quadrilaterals have special names.
Special Quadrilaterals
Diagram
Trapezoid
A trapezoid is a quadrilateral with exactly
1 pair of parallel sides.
Parallelogram
A parallelogram is a quadrilateral with
2 pairs of parallel sides.
Rectangle
A rectangle is a parallelogram with
4 right angles.
Rhombus
A rhombus is a parallelogram with
4 congruent sides.
Square
A square is a parallelogram with
4 right angles and 4 congruent sides.
EXAMPLE
with
Notetaking
To help you classify
quadrilaterals, you could
draw a diagram that
shows how the special
quadrilaterals are related
to each other.
1
Classifying a Quadrilateral
Sketch and classify a quadrilateral with opposite sides parallel, one
side of length 3 cm, and another side of length 1 cm.
3 cm
1 Draw two sides, one of length 3 cm
1 cm
and one of length 1 cm. The angle
between the two sides does not matter.
2 Draw sides parallel to the first two
sides to complete the figure.
ANSWER The figure is a parallelogram.
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Chapter 10
Geometric Figures
3 cm
1 cm
1 cm
3 cm
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Your turn now
Sketch and classify the quadrilateral described.
1. A quadrilateral with 4 right angles, 4 congruent sides of length
2.5 centimeters, and both pairs of opposite sides parallel
Polygons A polygon is a geometric figure that is made up of three or
more line segments that intersect only at their endpoints. The number
of sides determines the name of the polygon.
Classifying Polygons
with
Reading
The prefixes used in the
names of polygons tell you
the number of sides the
figure has.
Prefix
triquadpentahexaheptaocta-
Meaning
three
four
five
six
seven
eight
EXAMPLE
Triangle
Quadrilateral
Pentagon
3
sides
4 sides
5 sides
Hexagon
Heptagon
Octagon
6 sides
7 sides
8 sides
2
Classifying Polygons
Tell whether the figure is a polygon. If it is, classify it. If it is not,
explain why not.
a.
b.
Solution
a. This figure is a polygon
with 5 sides. So, it is
a pentagon.
b. This figure is not a polygon
because it is not made up
entirely of line segments.
Your turn now
Tell whether the figure is a polygon. If it is, classify it.
If it is not, explain why not.
2.
3.
4.
Lesson 10.4
Polygons
495
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Regular Polygons A regular polygon is a polygon with
all sides equal in length and all angles equal in measure.
The pentagon shown is an example of a regular polygon.
tch Out!
Wa
Just because a
polygon has sides that are
all congruent does not
necessarily mean that it
is a regular polygon. All
angles must also be
congruent.
EXAMPLE
3
Using a Regular Polygon
The polygon shown is a regular pentagon. Find the
perimeter of the pentagon. Then find the sum of the
angle measures in the pentagon.
1 A regular pentagon has 5 sides of equal length, so
the perimeter of the pentagon is 5(3) 15 feet.
3 ft
2 A pentagon can be divided into three triangles. The sum of the
angle measures in a triangle is 180, so the sum of the angle
measures in any pentagon is 180 180 180 540.
INTERNET
Exercises
eWorkbook Plus
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More Practice, p. 714
Getting Ready to Practice
1. Vocabulary Copy and complete: Two types of quadrilaterals that have
four right angles are _?_ and _?_.
Tell whether the figure is a polygon. If it is a polygon, classify it. If
it is not, explain why not.
2.
3.
4.
5. Guided Problem Solving The quilt design shown repeatedly uses
regular hexagons and other polygons. What is the sum of the angle
measures in a hexagon?
1 Sketch a hexagon on a piece of paper.
2 Draw three line segments to divide the hexagon into triangles.
3 Use the triangles to find the sum of the angle measures in a
hexagon.
496
Chapter 10
Geometric Figures
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
Homework
Use the clues to sketch and classify the quadrilateral described.
Exercises
6–8
9–16
21–22
6. This figure has four right angles. Not all of the sides are the same
Online Resources
8. This figure has exactly one pair of opposite sides that are parallel.
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• More Examples
• eTutorial Plus
length.
7. This figure’s opposite sides are parallel and congruent. Not all of the
angles are congruent.
Classify the polygon and tell if it is regular. If it is not regular,
explain why not.
9.
10.
11.
12.
13.
14.
15. Stained Glass Window Sketch and classify
four different polygons contained in the
stained glass window. Do any of the polygons
appear to be regular? Explain your reasoning.
16. Geometry Graph and connect the ordered
pairs (0, 5), (3, 2), (2, 2), (2, 1), (3, 2),
and (0, 5) in the order they are given. Is the
figure that results a polygon? If it is, classify it
and tell if it is regular. If it is not a polygon,
explain why not.
Critical Thinking Tell whether the statement is true or false.
Explain your reasoning.
17. All squares are rectangles.
18. A scalene triangle is regular.
19. A trapezoid is a parallelogram.
20. Every rhombus is a square.
Find the measure of each side of the polygon described.
21. A regular octagon with a perimeter of 46 centimeters
22. A regular heptagon with a perimeter of 52.5 inches
Lesson 10.4
Polygons
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Extended Problem Solving In Exercises 23–26, you will examine the
angle measures of polygons.
23. Break into Parts Copy and complete the table below. Use the problem
solving strategy of breaking into parts.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Sum of angle measures
?
?
?
?
Measure of each angle
in a regular polygon
?
?
?
?
24. Look for a Pattern What pattern do you notice in the sum of the angle
measures in the table?
25. Predict Use the pattern you identified to predict the sum of the angle
measures in a heptagon. What do you predict is the measure of each
angle in a regular heptagon?
26. Challenge Write an expression for the sum of the angle measures in a
regular polygon with n sides. Then write an expression for the measure
of each angle in a regular polygon with n sides.
27. Critical Thinking Name a quadrilateral that is always a regular
polygon. Explain your reasoning.
Mixed Review
28. Your average monthly checking account balance was $580 in January
and $957 in March. What was the percent of increase in your account
balance from January to March? (Lesson 9.6)
29. Classify a triangle that has angle measures of 25, 105, and 50.
(Lesson 10.3)
Basic Skills Evaluate the power.
30. 23
31. 3 2
32. 18
33. 54
Test-Taking Practice
INTERNET
State Test Practice
34. Multiple Choice What is the sum of the angle measures in a
parallelogram?
CLASSZONE.COM
A. 360
B. 270
C. 180
D. 90
35. Multiple Choice What is the perimeter of a regular octagon with a
side length of 4 centimeters?
F. 12 cm
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Chapter 10
Geometric Figures
G. 16 cm
H. 32 cm
I. 64 cm