ABCD is a parallelogram where ∠ADP=∠CBQ=90∘\angle ADP = \angle CBQ = 90^\circ∠ADP=∠CBQ=90∘, also ABP and QDC are straight lines. Prove that △ADP\triangle ADP△ADP is congruent to △CBQ\triangle CBQ△CBQ. Also, explain why AQ is parallel to PC.