The Polygon Angle-Sum Theorems Worksheet With Answers Page 2
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82. Teach
You can classify a polygon by the number of sides it
Name
Sides
has. The table at the right shows the names of some
3
triangle
common polygons.
4
quadrilateral
Polygons are classified as convex or concave.
Guided Instruction
A
D
5
pentagon
Vocabulary Tip
A
convex polygon
6
hexagon
A diagonal of a polygon is
R
Y
has no diagonal
1
1
Math Tip
EXAMPLE
EXAMPLE
a segment that connects
with points outside
8
octagon
two nonconsecutive
the polygon.
T
Remind students that there are
vertices.
9
nonagon
also different ways to name sides
Diagonal
10
decagon
and angles in this example. Ask:
M
P
concave polygon
A
12
dodecagon
What is another name for
HK
?
has at least one
K
G
W
Q
KH
What is another name for
diagonal with points
n
n-gon
lKMG or lGMK
outside the polygon.
&M?
S
Connection to Science
In this textbook, a polygon is convex unless stated otherwise.
The study of optics teaches that
a convex lens causes rays of light
to come together and that a
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2
Real-World
Connection
EXAMPLE
EXAMPLE
concave lens causes rays of light
to spread apart. Convex lenses
Tilework
The tilework in the photo is a combination of different polygons that
are used in microscopes and
form a pleasing pattern. Classify the polygon outlined in red by using the table
telescopes. Eyeglasses may be
above. Then classify the polygon as convex or concave.
either convex or concave.
Teaching Tip
Students may want to know that
a seven-sided polygon is called a
heptagon.
Visual Learners
To help students learn the names
of polygons, have small groups
make charts to be displayed in
the classroom with the name of
each polygon, its number of sides,
and an appropriate figure.
PowerPoint
The polygon outlined in red has 6 sides. Therefore, it is a hexagon.
Additional Examples
No diagonal of the hexagon contains points outside the hexagon. The hexagon
is convex.
1
1
Name the polygon. Then
Quick Check
identify its vertices, sides, and
2
2
Classify each polygon by its sides. Identify each as convex or concave.
angles.
a.
b.
A
octagon; concave
hexagon; convex
E
B
D
C
c. the 12-pointed star at the center of the tilework pictured above
24-gon; concave
ABCDE; vertices: A, B, C, D, E;
sides:
AB
,
BC
,
CD
,
DE
,
EA
;
angles: lA, lB, lC, lD, lE
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Chapter 3
Parallel and Perpendicular Lines
2
2
Classify the polygon below by
its sides. Identify it as convex or
concave.
dodecagon; concave
Advanced Learners
L4
English Language Learners
ELL
Have students do the Activity, discuss whether
Some students may not know the meaning of
Theorem 3-14 applies to concave n-gons, and justify
adjacent sides in the definition of a polygon. Show
their reasoning.
how adjacent sides share a vertex just as adjacent
angles share a side
learning style: verbal
learning style: visual
158
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