Page 56 - Maths Class 06

Plane
Can you give an example of a plane in the things around you? This question should not bother, you as the
floor of your room, the top of your dinner table, the cover of a book, etc., are all examples of a plane. A
plane is defined as a flat surface that extends indefinitely in all directions. A room has six planes
represented by its four walls, floor and ceiling. All the six planes of the room can be extended indefinitely.
Parallel Planes

Just like parallel lines, the parallel planes also do not meet each other no matter how long they are
extended.
For ex am ple, the floor and ceil ing of a room are two par al lel planes.

Intersecting Planes
Some planes, like the adjacent wills of a room, meet each other. Such planes are called intersecting
planes. Whenever two planes intersect, they intersect at a line. In a room, the two planes, represented by
its adjacent walls, intersect to form an edge of the room. The edge is like a line.

Open and Closed Curves

A figure having a certain area enclosed inside it, is called a closed figure. Some closed figures are given
alongside:

Fig. 4.9
A figure whose sides (or boundary) do not close any area inside, is called an open figure. Some open
figures are given alongside:

Fig. 4.10
In these curves, there are some which end at the same place they started from. Here, such curves are (b),
(d), (g) and (h).
A curve which begins and ends at the same point is called a closed curve; others are called open curves.

Interior and Exterior of a Closed Figure

A figure divides the plane into three parts. Look at the given figure. U
P S
1. The shaded part which lies inside forms the inte rior of the figure. A
W C
In other way, we say that the part formed by all points like A B C, , , Interior V
etc. which are enclosed in the figure forms the interior of the
B
figure. Q
X R Exterior
Fig. 4.11
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