9th karnataka state syllubus

1. POLYGONS

2. Definition of polygons
• A Polygon is any flat shape with three or
more sides. Polygons are closed figures,
which means that the lines are closed and
not open.

3. Types of
Polygons

4. 1. Simple and complex polygons
• A simple polygon has only one boundary and the
sides do not cross each other, otherwise it is a
complex polygon.

5. • Simple polygon
• Complex polygon

6. 2. Concave and convex polygons
• A convex polygon has no internal angle more than
180º and if there are any internal angles greater
than a straight angle, then it is a concave polygon.

7. • Concave polygon
• Convex polygon

8. 3. Regular and Irregular polygons
• Regular polygon is one whose sides are all equal and
whose interior angles are all congruent. Thus, a regular
polygon is both equilateral and equiangular. If, otherwise,
the polygon is said to be irregular polygon.

9. • Regular polygon

11. • Irregular polygon

12. • Irregular polygon

13. NAMES OF
POLYGONS

14. • Polygons are named or classified
according to their number of
sides. A polygon with n sides is
called n-gon.

15. n (sides) Polygon
3 Triangle, trigon
4 Quadrilateral, tetragon
5 Pentagon
6 Hexagon
7 Heptagon
8
9
Octagon
Nonagon, enneagon
10 Decagon

16. Sides Polygon
11 Hendecagon
12 Didecagon
Tridecagon13
14 Tetradecagon
15 Pentadecagon
16 Hexadecagon
17 Heptadecagon
18 Octadecagon
19 Enneadecagon
20 Icosagon

17. • To construct a polygon’s name, combine the
corresponding prefix and suffix.
Example:
Construct the name for 28 and 46 sided
polygons.
20
Sides Prefix
Icosa
Sides Suffix
8 Octagon
Icosaoctagon

18. Sides Prefix Sides Suffix
40 tetracon 6 hexagon
Tetraconhexagon

19. Angle – sum property of a polygon
• Proposition 1 : if a polygon has n sides & if all
possible diagonals are drawn from any fixed
vertex, there will be a total of ( n-2) triangles
are formed
• Example : if all possible diagonals are drawn to
a pentagon. Then how many triangles are
formed in pentagon?
Pentagon has 5 sides , n=5
Total no of triangles are formed = 5-2 = 3

20. Proposition -2
• The sum of interior angles of a polygon with n
sides is equal to (2n-4) right angles or (n-2)
straight angles.
• Example : Find the sum of interior angles of
Hexagon.
– Sum of all interior angles of a Hexagon = (n-2) straight angles.
= (6-2) 180
= 4× 180
=720°.

21. Corollary 1
• In a regular polygon with n sides, each interior
angle is equal to
(𝑛−2)
𝑛
180°
• Example : Find the each interior angle of a
pentagon.
– Each interior angle=
(𝑛−2)
𝑛
180
=
(5−2)
5
180
=
3
5
180
= 3× 36
= 108°

22. Proposition 3
• Sum of all its exterior angles = 2n – (2n-4)
right angles = 4 right angles
• Carollary 2 :
• “ in a regular polygons all its exterior angles
are equal to
360
𝑛
angles”.

23. Exercise 4.1.3
• 1. In each of the following ploygons find in
degrees the sum of the interior angles and
the sum of exterior angles.
• (i) Hexagon (ii) Octagon (iii) pentagon
– (iv) Nanogon ( v)