What is a Polygon? Classification of Polygons. Convex and Concave polygons, Regular and
Irregular polygons. Angle sum property of a quadrilateral. Kinds of quadrilaterals and their
properties.
Answers
Step-by-step explanation:
A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. The line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed. An example of a polygon is a triangle with three sides.
Depending on the sides and angles, the polygons are classified into different types, namely:
• Regular Polygon
• Irregular Polygon
• Convex Polygon
• Concave polygon
Regular Polygon
If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon. The examples of regular polygons are square, rhombus, equilateral triangle, etc.
Irregular Polygon
If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon. For example, a scalene triangle, a rectangle, a kite, etc.
Convex Polygon
If all the interior angles of a polygon are strictly less than 180 degrees, then it is known as a convex polygon. The vertex will point outwards from the centre of the shape.
Concave Polygon
If one or more interior angles of a polygon are more than 180 degrees, then it is known as a concave polygon. A concave polygon can have at least four sides. The vertex points towards the inside of the polygon.
However, a number of polygons are defined based on the number of sides, angles and their properties. Let us see one of the frequently used and the primary type of polygon, i.e. triangle.
According to the angle sum property of a Quadrilateral, the sum of all the four interior angles is 360 degrees.
Proof: In the quadrilateral ABCD,
∠ABC, ∠BCD, ∠CDA, and ∠DAB are the internal angles.
AC is a diagonal
AC divides the quadrilateral into two triangles, ∆ABC and ∆ADC
We have learned that the sum of internal angles of a quadrilateral is 360°, that is, ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.
There are basically five types of quadrilaterals. They are;
Parallelogram: Which has opposite sides as equal and parallel to each other.
Rectangle: Which has equal opposite sides but all the angles are at 90 degrees.
Square: Which all its four sides as equal and angles at 90 degrees.
Rhombus: Its a parallelogram with all its sides as equal and its diagonals bisects each other at 90 degrees.
Trapezium: Which has only one pair of sides as parallel and the sides may not be equal to each other.
Answer:
a polygon is a 2 dimensional figure