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∘ [∵ XA⊥AB]
And ∠YBA=90∘ [∵ YB⊥AB]
∴ ∠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.]