No correct solutions have been received for this problem this month. Why not try dropping a perpendicular from Q to AB and use similar triangles?

Parallel Universe - a step towards the solution

It is easy to assume things that you do not know for certain. David (from Madras College) has offered a solution that has helped me come up wite the following advice tha might help.

Take care not to make assumptions!

Draw a line perpendicualr for AB through A

Produce DQ to meet the perpendicular through A at X.

Let the point of intersection of BC and DQ be Y.

Can you show that AXQ is congruent to DYQ?

If you can you should be able to show that AB is parallel to QD.