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Question 2
Draw a line segment AB of 4cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

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Solution

To draw a line perpendicular to AB through A and B, respectively, use the following steps of construction.
(i) Draw a line segment AB = 4cm.
(ii) Taking A as the centre and radius more than 12 AB(i.e., 2cm) draw an arc which intersects AB at E.
(iii) Taking E as the centre and with the same radius as above draw an arc which intersects the previous arc at F.
(iv) Again, taking F as the centre and with the same radius as above draw an arc which intersects previous arc( obtained in step (ii)) at G.

(v) Taking G and F are centres, draw arcs which intersect each other at H.
(vi) Join AH, thus AX is the perpendicular to AB at A. similarly, draw BY AB at B.
Now, we know that if two lines are parallel, then the angle between them will be 0 or 180.
Here, XAB=90 [ XAAB]
And YBA=90 [ YBAB]
XAB+YBA=90+90=180
So, the lines XA and YB are parallel.
[ since, if the sum of interior angles on same side of transversal is 180, then the two lines are parallel.]

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