Page 76 - Maths Class 06

Perpendiculars Lines
In the previous chapter, we have learnt about intersecting and P P
parallel lines.

Two intersecting lines are said to be per pen dic u lar if they meet
R S R S
each other at right angles. O O

« «
e g. ., PQ and RS are two lines that intersect each other at right
Q Q
angles. Fig. 5.2

\ PQ is perpendicular to RS.
It is written as PQ ^ RS.
« « «
If RS is a line segment and PQ is perpendicular to RS at a point O such that O is midpoint of RS; then PQ is
«
called the perpendicular bisector of RS. Fig. 5.2

EX AM PLE 1. Study the num ber line given be low. The line l is per pen dic u lar to line m.

A B C D E F G H I
l
0 1 2 3 4 5 6 7 8 9

P
m

(a) Is CE = EG?
(b) Does PE bisect CG?

(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG (ii) CD = GH (iii) BC < EH

SOLUTION : (a) Yes, CE = EG = 2 units.
(b) Yes, PE does bisect CG as CE = EG proved in (i).
(c) PE is perpendicular bisector of DF and CG.
(d) (i) AC > FG true as AC = 2 units, FG = 1 unit.

(ii) CD = GH true as CD = 1 unit, GH = 1 unit.
(iii) BC < EH true as BC = 1 unit, EH = 3 units.

Exercise 5.3

1. Draw AB = 8 cm. Mark a point O on it, with the help of the protractor, draw PO ^ AB.

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