meaning of polygon explained with all shapes and other info.
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A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are allexamples of polygons. The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides.
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Polygon➡ A simple closed plane figure bounded by line segments is called a polygon. The line segment has called its sides and the points of intersection of consecutive sides are called its vertices.
☆A polygon has the same number of angles as it has sides.
☆ A polygon is named according to the number of sides/ angles it has.
Diagnol of a polygon
➡Line segment joining any two consecutive vertices of a polygon is called its diagonal.
Convex Polygon: If all the interior angles of a polygon are less than 180 degree it is called a convex polygon.
Concave Polygon: If one or more of the interior angles of a polygon is greater than 180 degree that is reflex it is called a concave polygon.
Exterior angle of a convex polygon:
If we produce the side of a polygon the angle it makes with the left side is called an exterior angle.
Remember, An exterior angle + adjacent interior angle = 180 °
Regular Polygon
➡ A polygon is called regular polygon if all its sides have equal length and all its animals have equal size.
Thus, in a regular polygon:
☆ all sides are equal in length
☆all interior angles are equal in size.
☆ all exterior angles are equal in size.
Note➡ All regular polygons are convex.
ANGLE PROPERTY OF A POLYGON:
☆Sum of interior angles of a polygon
➡ The sum of interior angles of a polygon of n sides = (2n - 4) right angles.
☆ Sum of interior angles of a quadrilateral
➡The sum of interior angles of a quadrilateral = 360°
☆Sum of exterior angles of a convex polygon.
➡ the sum of exterior angles of a convex polygon is = 360°
From above results it follows that:
➡Each interior angle of a regular polygon of n sides = 2n - 4/n right angles.
➡Each exterior angle of a regular polygon of n sides equals = 360°/n
➡ If each exterior angle of a regular polygon is x° degree then the number of the sides in the regular polygon = 360/ x
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☆A polygon has the same number of angles as it has sides.
☆ A polygon is named according to the number of sides/ angles it has.
Diagnol of a polygon
➡Line segment joining any two consecutive vertices of a polygon is called its diagonal.
Convex Polygon: If all the interior angles of a polygon are less than 180 degree it is called a convex polygon.
Concave Polygon: If one or more of the interior angles of a polygon is greater than 180 degree that is reflex it is called a concave polygon.
Exterior angle of a convex polygon:
If we produce the side of a polygon the angle it makes with the left side is called an exterior angle.
Remember, An exterior angle + adjacent interior angle = 180 °
Regular Polygon
➡ A polygon is called regular polygon if all its sides have equal length and all its animals have equal size.
Thus, in a regular polygon:
☆ all sides are equal in length
☆all interior angles are equal in size.
☆ all exterior angles are equal in size.
Note➡ All regular polygons are convex.
ANGLE PROPERTY OF A POLYGON:
☆Sum of interior angles of a polygon
➡ The sum of interior angles of a polygon of n sides = (2n - 4) right angles.
☆ Sum of interior angles of a quadrilateral
➡The sum of interior angles of a quadrilateral = 360°
☆Sum of exterior angles of a convex polygon.
➡ the sum of exterior angles of a convex polygon is = 360°
From above results it follows that:
➡Each interior angle of a regular polygon of n sides = 2n - 4/n right angles.
➡Each exterior angle of a regular polygon of n sides equals = 360°/n
➡ If each exterior angle of a regular polygon is x° degree then the number of the sides in the regular polygon = 360/ x
____________ Thank You_______________
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