Page 164 - Ganit Kaushal

Closed Curves: In the plane, closed curves are those whose
starting point is also their end point. In the figures, (i), (iii), (v), Note
and (vi) on the previous page are closed curves. In this chapter, a closed curve will
always mean a simple closed curve,
Simple Closed Curves: The closed curves that do not cross unless otherwise stated.
themselves are called ‘simple closed curves’. In the figures, (i)
and (v) on the previous page are simple closed curves.

Polygons

A figure is called a polygon if it is a simple closed figure (curve) made up entirely of line segments (all the
sides are joined up). Triangles, quadrilaterals, pentagons, etc., are all examples of polygons.

Regular Polygons and their Diagonals
D
Polygons with equal sides and equal angles are known as regular polygons. Their
diagonals are the line segments joining any two non-adjacent vertices. The adjoining E C
figure is an example of a regular polygon with five sides, known as a regular pentagon.
Here, we have sides AB = BC = CD = DE = EA and interior angles ∠A = ∠B = ∠C = ∠D
= ∠E and the line segments EC and EB are two of its diagonals. A B

Triangle

A polygon with three sides is called a triangle, and a regular polygon with
three sides is called an equilateral triangle. Adjoining figures (i) and (ii)
show a triangle and an equilateral triangle respectively. (i) Triangle (ii) Equilateral triangle

Parallelogram
L M
A quadrilateral with two pairs of parallel sides is called a parallelogram.
In the adjoining figure, quadrilateral LMNO is a parallelogram in which LM || ON and

LO || MN. The diagonals of a parallelogram bisect each other. Opposite angles of a O N
parallelogram are equal. Parallelogram

Rectangle P Q

A rectangle is a parallelogram with four right angles.

In the adjoining figure, PQRS is a rectangle in which ∠P = ∠Q = ∠R = ∠S = 90° and
PS = QR and PQ = SR. The diagonals of a rectangle are equal. S R
Rectangle
Square M O

A regular polygon with four equal sides and four right angles is called a square. In other words,
a square is a rectangle having all four sides equal. In the adjoining figure, MORE is a square in
which MO = OR = RE = EM and ∠M = ∠O = ∠R = ∠E = 90°. The diagonals of a square are E R
equal and bisect each other. Square

162 Mathematics-6