Yes, the both ray Qx and Ry are parallel to each other

on any line when we draw perpendiculars from any point on the line, all the perpendiculars are always parallel to each other.
if u have to prove it than take a point on the ray Qx and another point on ray Ry of the same distance (let us take the point as A and B on ray Qx and Ry). and then join both the points to R and Q(join A to R and B to Q). then u find two right angle triangle on the same base QR. then prove both the triangles congruent as
QR=QR (common)
AQ=BR (we had taken)
angle Q= angle R [perpendicular (90°)]
∴ by SAS both the triangles are congruent.

if the diagonal of the two triangles is equal which are on the same base then the other third side (AQ and BR)of the triangle are parallel. 

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