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 centre and radius more than `(1)/(2)AB` (i.e., 2 cm) draw an arc say it intersect AB at E.
(iii) Taking E as centre and with same radius as above draw an arc which intersect previous arc at F.
(iv) Again, taking F as centre and with same radius as above draw an arc which intersect 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 perpendicular to AB at A. Similarly, draw `BY bot AB` at B Now, we know that if two lines are parallel , then the angle between then will be `0^(@) or 180^(@)` .
Here, `angleXAB = 90^(@) [becauseXA bot AB]`
and `angleYBA = 90^(@) [becauseYB bot AB]`
`:.angleXAB + angleYBA = 90^(@) + 90^(@) = 180^(@)`
So, the lines XA and YB are parallel.
[since, it sum of interior angle on same side of transversal if `180^(@)` , then the two lines are parallel]
