G. 04.02 Geometry (9) || ज्यामितीय || Polygon (2) Polygon And Its Part
By
Om Jitender Singh Tomar
(ॐ जितेन्द्र सिंह तोमर)
M.A., B.Ed., DNYS, MASSCOM
11/1/10/1/2022
Polygons
A simple closed curve made up of only line segments is called a polygon.
Regular and irregular polygons
Regular polygon
A polygon with equal sides and angle is called regular polygon.
For example,
Equilateral Triangle is three sided irregular polygon and a square is four sided irregular polygon because of sides of equal length and angles of equal measure.
Irregular polygon
A polygon with unequal sides and unequal angle is called irregular polygon.
A rectangle a irregular polygon
Classification of polygons
We classify polygons according to the number of sides (or vertices) they have.
3 – sides Polygon Triangle
4 – sides Polygon Quadrilateral
5 – sides Polygon Pentagon
6 – sides Polygon Hexagon
7 – sides Polygon Heptagon
8 – sides Polygon Octagon
9 – sides Polygon Nonagon
10 – sides Polygon Decagon
n – sides Polygon n-gon
Diagonals
A line segment connecting two non-consecutive [or Opposite] vertices of a polygon is called a diagonal.
No. of Diagonals = Sides (Sides – 3)/2
No. of Diagonals in Triangle
Sides= 3
No. of Diagonals = Sides (Sides – 3)/2
= 3 (3 – 3)/2
= 3 (0)/2
= 0
No. of Diagonals in quadrilateral
Sides= 4
No. of Diagonals = Sides (Sides – 3)/2
= 4 (4 – 3)/2
= 4 (1)/2
= 4/2
= 2
No. of Diagonals in Pentagon
Sides= 5
No. of Diagonals = Sides (Sides – 3)/2
= 5 (5 – 3)/2
= 5 (2)/2
= 10/2
= 5
Angle sum property
The sum of the measures of the three angles of a triangle is 180°.
Angle sum of a polygon
[No. of the Sides – 2] = 180⁰
Angle sum property of Triangle [ASPOT]
Sides= 3
Angle sum of Triangle = (Sides – 2)180⁰
= (3 – 2)180⁰
= (1)180⁰
= 180⁰
Angle sum property of Quadrilateral [ASPOQ]
Sides= 4
Angle sum of Quadrilateral = (Sides – 2)180⁰
= (4 – 2)180⁰
= (2)180⁰
= 360⁰
Angle sum property of Pentagon [ASPOP]
Sides= 4
Angle sum of Pentagon = (Sides – 2)180⁰
= (5 – 2)180⁰
= (3)180⁰
= 540⁰
Sum of the Measures of the Exterior Angles of a Polygon
The sum of the measures of the external angles of any polygon is 360°.
m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360°
Sum of the Measures of the Exterior Angles of a regular Polygon
The sum of the measures of the external angles of any regular polygon is 360°.
No. of sides × measure of exterior angle = 360°
(i)
No. of sides = 360° /Measure of exterior angle
(ii)
Measure of exterior angle = 360°/No. of sides
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