1. Sketch an example of a convex heptagon and an example of a concave heptagon.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 75E
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Can you help me with 1 and 2 please 

CLASSIFYING POLYGONS A polygon is named by the number of its sides.
Number of sides
Type of polygon
Number of sides Type of polygon
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
Pentagon
10
Decagon
Нехagon
12
Dodecagon
7
Heptagon
n-gon
The term n-gon, where n is the number of a polygon's sides,
can also be used to name a polygon. For example, a polygon
with 14 sides is a 14-gon.
In an equilateral polygon, all sides are congruent.
In an equiangular polygon, all angles in the interior
of the polygon are congruent. A regular polygon is a
convex polygon that is both equilateral and equiangular.
regular pentagon
EXAMPLE 2
Classify polygons
READ DIAGRAMS
..... ..********
Double marks are used
Classify the polygon by the number of sides. Tell whether the polygon is
equilateral, equiangular, or regular. Explain your reasoning.
in part (b) of Example 2
to show that more than
a.
b.
с.
one pair of sides are
congruent and more
than one pair of angles
are congruent.
%23
Solution
a. The polygon has 6 sides. It is equilateral and equiangular, so it is a
regular hexagon.
b. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or
equiangular, so it is not regular.
c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so
it is equilateral. The polygon is not convex, so it is not regular.
Animated Geometry at my.hrw.com
GUIDED PRACTICE
for Examples 1 and 2
1. Sketch an example of a convex heptagon and an
example of a concave heptagon.
2 m
2. Classify the polygon shown at the right by the
umber of sides. Explain how you know that
the sides of the polygon are congruent and that
the angles of the polygon are congruent.
2 m
2 m
2 m
1.6 Classify Polygons
43
Transcribed Image Text:CLASSIFYING POLYGONS A polygon is named by the number of its sides. Number of sides Type of polygon Number of sides Type of polygon 3 Triangle 8 Octagon 4 Quadrilateral 9 Nonagon Pentagon 10 Decagon Нехagon 12 Dodecagon 7 Heptagon n-gon The term n-gon, where n is the number of a polygon's sides, can also be used to name a polygon. For example, a polygon with 14 sides is a 14-gon. In an equilateral polygon, all sides are congruent. In an equiangular polygon, all angles in the interior of the polygon are congruent. A regular polygon is a convex polygon that is both equilateral and equiangular. regular pentagon EXAMPLE 2 Classify polygons READ DIAGRAMS ..... ..******** Double marks are used Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. in part (b) of Example 2 to show that more than a. b. с. one pair of sides are congruent and more than one pair of angles are congruent. %23 Solution a. The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. b. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular. Animated Geometry at my.hrw.com GUIDED PRACTICE for Examples 1 and 2 1. Sketch an example of a convex heptagon and an example of a concave heptagon. 2 m 2. Classify the polygon shown at the right by the umber of sides. Explain how you know that the sides of the polygon are congruent and that the angles of the polygon are congruent. 2 m 2 m 2 m 1.6 Classify Polygons 43
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