Question

draw a line segment QR = 5 cm construct perpendicular at point Q and R to it. Name them as Qx and Ry respectively are they both parellel

Answer 1

Given transversal and two lines, for the two lines to be parallel, one of the following conditions must be met:
1. a pair of alternate angles must be congruent
2. a pair of corresponding angles must be congruent
3. co-interior angles must be Supplementary.

In this case, given lines are Qx and Ry and line QR is the transversal. 
∠Q = ∠ R = 90°  --- by construction

∠Q + ∠ R  = 90 + 90 = 180°
Hence we can say that Qx and Ry are parallel as the co interior angles are supplementary

Answer 2

If two parallel lines are cut by transversal 
the interior angles are supplementary(i.e. their sum is equal to 180)
here Qx and Ry are perpendicular to QR
so the inerior angles are angle(xQR) and angle(yRQ)
angle(xQR)=angle(yRQ)=90
=>  angle(xQR) + angle(yRQ) = 180
which means the interior angles are supplementary
so Qx is parallel to Ry