Question

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

Answer 1

Draw a line perpendicular to AB through A and B

Draw $\mathrm{AB}$$=4cm$ and considering A as the centre, draw an arc, cutting $\mathrm{AB}$ at $\mathrm{P}$ . Considering $\mathrm{P}$ as a centre and the same radius, draw an arc cutting the arc drawn at $\mathrm{Q}$ and then Considering $\mathrm{Q}$ as a centre and the same radius, draw an arc, cutting the arc drawn at $\mathrm{R}$

Considering $\mathrm{R}$ as the centre and the same radius, draw an arc, cutting the arc drawn at $\mathrm{X}$ and Draw and produced it to C and D.

Similarly we can draw the line $\mathrm{EF}$ perpendicular through $\mathrm{B}$

Thus, the given lines are parallel because the sum of the interior angles on the same side of the transversal is $180°$.