Given: Angle PQT and angle RQT are right angles, Line PQ is congruent to line QR, Angle VQT is congruent to angle SQT.
Prove: Line VQ is congruent to line SQ.
I have tried to construct a diagram based on your description, but there are many posibilities. Do these lines produce closed figures like triangles, rectangles, etc.? See my figure and see if it's close to what you have described. If not, then enhance your description a bit.