Submitted by; SARANGI.PS Mathematics Kaviyattu College Of Education, Pirappancode
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MATHEMATICS
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Dear children, I prepared the digital textbook for all students who are interested to study mathematics. The textbook contains basic and some related areas regarding Polygons. I prepared this digital textbook as part of my B. Ed course. I dedicate this digital text to all pupils who are interested to study the topic Polygons
With love and regards Sarangi.PS Kaviyattu college of Education Pirappancode
Shapes Sum of Interior Angles Sum of Exterior Angles Regular polygons
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POLYGONS
Let’s observe the picture shown above … Can you differentiate the shapes you see here?
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SHAPES What are the different shapes that you have seen around you?
There are five different shapes are given and some among them shows some common characters. Identify the group with similarities and also identify the common characters among them…
These two shapes are open figures and one among them has 2 angles in it.
Here triangle is a closed figure with 3sides and 3 angles.
Rectangle id a closed figure with 4 sides and 4 angles.
Parallelogram is a closed figure with 4 sides and 4 angles.
Similarly, Pentagon is a closed figure with 5 sides and 5 angles.
Hexagon is a closed figure with 6 sides and 6 angles.
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Such closed shapes can commonly called as Polygons.
Polygons are the closed figures with three or more sides.
STRANGE POLYGONS Which is the smallest polygon that you have seen? Draw a polygon with 8 sides, what is it called?
Draw a triangle with sides as your wish, measure the angles of it and find the sum of its inner angles…
SUM OF INTERIOR ANGLES Do you remember the inner angles sum of a triangle? The sum of inner angles of any triangle is 180 ̊. Similarly, can we find the sum of interior angles of a quadrilateral?
Draw any quadrilateral and also draw any of its diagonals.
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0 0 2 2 These are also drawn 2 with straight lines only. Hence these are also 2 sometimes considered as polygon. 2 But in our lesson, we 2 do not include such figures in which 2 the vertices are sunken in, or whose 2 sides cross each other, as polygons.0This is because many of the principles 0 we want to generalize do not apply to them. 0
Now we can see two triangles here. The angle sum of a triangle is 180 ̊ then the inner angle sum of a quadrilateral is 2x 180 ̊ =360 ̊ now look at the pentagon shown below,
Draw two diagonals to the alternate vertices.
How many triangles can you see here? What is the inner angle sum of a triangle? Then find the sum of interior angles of a pentagon?
Now find the sum of interior angles of a hexagon like this? polygons triangle
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Number of triangles 1
quadrilateral
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2x180=360 ̊
pentagon
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3x180=540 ̊
hexagon
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4x180=720 ̊
---------------n
---------------------n-2
--------------------(n-2)x180 ̊
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figure
-----------------Polygon with ‘n’ number of sides
Number of sides
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Sum of interior angles of polygon 1x180=180 ̊
The sum of interior angles of any polygon is (n-2) x 180 ,̊ where n is the number of sides of the polygons
ACTIVITIES Draw polygon with ten sides, find the sum of interior angles of it? Find the sum of interior angles of a polygon with sides 52? The interior angles sum of polygon is 12240. Find the number of sides of the polygon? All the angles of a polygon with 20 sides are equal. Find the value of one of them?
SUM OF EXTERIOR ANGLES Draw a triangle and extent one of its sides
The angle shown in the figure is called an exterior or outer angle of the triangle. Similarly, we can draw extended lines from each vertex of the triangle
Here we can see each pair of the extrrior and corresponding interior angles make a linear pair. That is, the some of each pair is 180 ̊. Therefore, the total sum of the linear pairs is 3x180= 540 Here we have a triangle with sum of interior angles 180 ̊. Therefore, the sum of outer angles of triangles =540-180= 360 ̊ now look at aquadrilateral; 12
Number of linear pairs
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Sum of the angles of linear pairs = 4x180 = 720 ̊ Sum of interior angles
= 360 ̊
Sum of exterior angles
= 720-360 = 360 ̊
Sum of exterior angles of a quadrilateral = 360 ̊
➢ Similarly, try to find out the sum of exterior angles of a pentagon and hexagon
The sum of exterior angles of any polygon is 360 ̊
ACTIVITIES Find the value of one outer of a polygon with 24 sides whose all outer angles are equal? Can we draw a polygon whose sides are equal and with all of its outer angles are 6 ?̊ What about 7 ̊? The sum of outer angles of a polygon id double of the sum of its inner angles. How many sides does the polygon have?
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REGULAR POLYGONS What is an equilateral triangle? It is a triangle with all of its sides and all angles are equal. One of the angle is 60 ̊. Likewise, a square is a rectangle whose all sides are equal. An angle of a square is 90 ̊. Now look into a pentagon with all of its sides are equal. One of the angle of this pentagon is = 540/5= 108 ̊
➢ What about a hexagon with all of its sides are equal? Any polygon whose sides are in same length having the value of all of its angles equal. Such polygons are called Regular polygons.
Regular polygons are the polygons equal length of sides and equal angles.
ACTIVITIES ➢ Find the angle of a regular polygon of 15 sides? Also find the value of one outer angle? ➢ The angle of a regular polygon is 168 ̊. Find how many sides does the polygon have? ➢ check whether we can draw a hexagon with all sides equal and all angles different?