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

Step 1:

Draw a line and mark AB=4cm

Step 2:

With A as center draw an arc that intersects the line at P and Q.

Similarly with B as center draw an arc that intersects the line at R and S.

Step 3:

With P as center and radius more than half of PQ draw an arc and with Q as center and equal radius draw an arc and let the arcs intersect at X.

Similarly, With R as center and radius more than half of RS draw an arc and with S as center and equal radius draw an arc and let the arcs intersect at Y.

Step 4:

Join AX and BY.

Yes the lines XX’ and YY’ are parallel to each other as they both are perpendicular to the same line AB.