Page 216 - Start Up Mathematics_8 (Non CCE)

14 Understanding Quadrilaterals

A plane surface is an unobstructed shape like a sheet of paper. A plane has no thickness and it extends
indefinitely. If a number of points on a plane surface are joined without breaking (i.e., without lifting the pencil)
and without retracing any part of the path except single points, the curve so formed is called a plane curve.
Plane curves are of four types—(a) simple curve, (b) closed curve, (c) open curve and (d) simple closed curve.

(a) Simple curve: A curve which does not cross itself except that if you draw it
the starting and stopping point may be same is called a simple curve
(Fig. 14.1). Fig. 14.1

(b) Closed curve: A curve which starts and stop at the same point is called a
closed curve (Fig. 14.2). Fig. 14.2

(c) Open curve: A curve which is not closed (i.e., whose starting and stopping
points are different) is called an open curve (Fig. 14.3).
Fig. 14.3
(d) Simple closed curve: A closed curve which passes through a given point only
once is called a simple closed curve (Fig. 14.4).

A polygon is a simple closed figure made up of line segments (Fig. 14.5(a)). Fig. 14.4

(a) Curves which are polygons (b) Curves which are not polygons
Fig. 14.5

Convex and Concave Polygons
Convex polygon (Fig. 14.6) is a simple polygon, where:
– each interior angle is less than 180º.
– the segment connecting any two points of the polygon is wholly contained in the interior of the polygon.

Fig. 14.6
Concave polygon (Fig. 14.7) is a simple polygon, that is not convex.
– It has at least one interior angle greater than 180º i.e., it has an indentation.
– It is always possible to locate two points of a concave polygon so that the segment connecting them is not
wholly contained in its interior.

Fig. 14.7