Page 88 - Maths Skill - 6

86 Maths

Definition of Geometrical Representation/ Figure Example
Concept Symbol
5. Plane: A plane is a flat surface that A D Surface of a black-
extends indefinitely in all directions. Plane ABCD board, table top, a sheet
It is a two-dimensional concept. or B C of paper etc.

Plane E or E
or
Plane PQR or P R
Q

l
PAIR OF LINES
Look at Figs. 6.1 (a) and (b). Two lines l and m m
are shown but there is a difference between the l
two figures. The two lines l and m in Fig. 6.1 (a) (b)
are crossing each other at A, i.e., the two lines A m
intersect each other at A, whereas line l and m in
Fig. 6.1 (b) will never cross each other. So, we (a)
have intersecting lines in Fig. 6.1 (a) and parallel Fig. 6.1
lines in Fig. 6.1 (b).
Let’s elaborate further.

Intersecting Lines: Two or more lines passing through a common point are called
intersecting lines. An example of intersecting line is shown in Fig. 6.2.
Parallel Lines: Look at Fig. 6.3 carefully. If you extend AB and CD A D
in both directions, will they meet at any point?
Fig. 6.2: Crossing roads The answer is No. So, two or more lines which will not meet even C

after extending in either direction are called parallel lines.
B
Fig. 6.3
In Fig. 6.4 (i) the two lines a and b are parallel to each other and are written as a || b (read as a is parallel to b) Or
they may be written as PQ || RS according to Fig. 6.4 (ii).

a
P
b
R
Q

(i) (ii) S
P Fig. 6.4

R S Perpendicular Lines: Two lines are said to be perpendicular if the angle between them

measure 90°. For example, two edges of blackboard are perpendicular to each other. In
Fig. 6.5, PQ is perpendicular to RS and is written as PQ ⊥ RS.
Q
Fig. 6.5