introduction and classification of polygons

Polygons The word
‘polygon’ is a
Greek word.
Poly
Poly means
many and
gon
gon means
angles.

Polygons
Polygons
• The word polygon
means “many angles”
• A two dimensional
object
• A closed figure

More about Polygons
• Made up of three or more
straight line segments
• There are exactly two sides that
meet at a vertex
• The sides do not cross each other
Polygons

These are not Polygons
Polygons

Terminology
Side: One of the line
segments that make up a
polygon.
Vertex: Point where two
sides meet.
Polygons

• Interior angle: An angle formed
by two adjacent sides inside the
polygon.
• Exterior angle: An angle formed
by two adjacent sides outside
the polygon.
Polygons

Interior angle
Exterior angle
Polygons

Let us recapitulate
Interior angle
Diagonal
Vertex
Side
Exterior angle
Polygons

Types of Polygons
• Equiangular Polygon: a polygon
in which all of the angles are
equal
• Equilateral Polygon: a polygon
in which all of the sides are the
same length
Polygons

• Regular Polygon: a polygon
where all the angles are
equal and all of the sides
are the same length. They
are both equilateral and
equiangular
Polygons

Examples of Regular Polygons
Polygons

A convex polygon: A polygon whose
each of the interior angle measures
less than 180°.
If one or more than one angle in a
polygon measures more than 180°
then it is known as concave polygon.
(Think: concave has a "cave" in it)
Polygons

IN TERIOR
ANGLES OF A
POLYGON
Polygons

Let us find the connection
between the number of
sides, number of diagonals
and the number of triangles
of a polygon.
Polygons

Quadrilateral
Pentagon
180
o 180
o
180
o
180
o
180
o
2 x 180o
= 360o
3
4 sides
5 sides
3 x 180
o
= 540
o
Hexagon
6 sides
180
o
180
o
180
o
180
o
4 x 180o
= 720o
4
Heptagon/Septagon
7 sides
180o
180o
180o
180o
180o
5 x 180o
= 900o
5
2
1 diagonal
2 diagonals
3 diagonals
4 diagonals
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
Quadrilateral 4 1 2 2 x180
0
= 360
0
360
0
/4
= 90
0
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
0
= 360
0
360
0
/4
= 90
0
Pentagon 5 2 3 3 x180
0
= 540
0
540
0
/5
= 108
0
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
0
= 360
0
360
0
/4
= 90
0
0
= 540
0
540
0
/5
= 108
0
Hexagon 6 3 4 4 x180
0
= 720
0
720
0
/6
= 120
0
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
0
= 360
0
360
0
/4
= 90
0
0
= 540
0
540
0
/5
= 108
0
0
= 720
0
720
0
/6
= 120
0
Heptagon 7 4 5 5 x180
0
= 900
0
900
0
/7
= 128.3
0
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
0
= 360
0
360
0
/4
= 90
0
0
= 540
0
540
0
/5
= 108
0
0
= 720
0
720
0
/6
= 120
0
0
= 900
0
900
0
/7
= 128.3
0
“n” sided
polygon
n Association
with no. of
sides
Association
with no. of
sides
Association
with no. of
triangles
Association
with sum of
interior
angles
Polygons

Regular
Polygon
No. of
sides
No. of
diagonals
No. of Sum of the
interior
angles
Each
interior
angle
Triangle 3 0 1 180
0
180
0
/3
= 60
0
0
= 360
0
360
0
/4
= 90
0
0
= 540
0
540
0
/5
= 108
0
0
= 720
0
720
0
/6
= 120
0
0
= 900
0
900
0
/7
= 128.3
0
“n” sided
polygon
n n - 3 n - 2 (n - 2) x180
0
(n - 2)
x180
0
/ n
Polygons

Septagon/Heptagon
Decagon Hendecagon
7 sides
10 sides 11 sides
9 sides
Nonagon
Sum of Int. Angles
900o
Interior Angle 128.6o
Sum 1260
o
I.A. 140
o
Sum 1440o
I.A. 144
o
Sum 1620o
I.A. 147.3
o
Calculate the Sum of Interior
Angles and each interior angle
of each of these regular
polygons.
1
2 4
3
Polygons

2 x 180o
= 360o
360 – 245 = 115o
3 x 180o
= 540o
540 – 395 =
145o
y
117o
121o
100o
125o
140o z
133o
137o
138o
138o
125o
105o
Find the unknown angles
below.
Diagrams not
drawn
accurately.
75o
100o
70o
w
x
115o
110o
75o
95o
4 x 180o
= 720o
720 – 603 =
117o
5 x 180o
= 900o
900 – 776 =
124o
Polygons

EXTERIOR ANGLES
OF A POLYGON
Polygons

An exterior angle of a regular polygon is
formed by extending one side of the polygon.
Angle CDY is an exterior angle to angle CDE
Exterior Angle + Interior Angle of a regular polygon =180
0
D
E
Y
B
C
A
F
1
2
Polygons

1200
1200
1200
600
600
600
Polygons

600
600
600
600
600
600
Polygons

1
2
3
4
5
6
600
600
600
600
600
600
Polygons

No matter what type of
polygon we have, the
sum of the exterior
angles is ALWAYS equal
to 360º.
Sum of exterior angles =
360º
Polygons

In a regular polygon with ‘n’
sides
Sum of interior angles = (n -2) x
180
0
Exterior Angle + Interior Angle
=180
0
Each exterior angle = 360
0
/n
No. of sides = 360
0
/exterior angle
Polygons

Let us explore few more
problems
• Find the measure of each interior angle of a
polygon with 9 sides.
• Ans : 140
0
• Find the measure of each exterior angle of a
regular decagon.
• Ans : 36
0
• How many sides are there in a regular polygon if
each interior angle measures 1650
?
• Ans : 24 sides
• Is it possible to have a regular polygon with an
exterior angle equal to 400
?
• Ans : Yes
Polygons

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introduction and classification of polygons

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