The bisectors of opposite angles are parallel to each other.
ABCD is aparallelogram.
AP bisects ∠A and CQ bisects ∠C.
Opposite angles of a parallelogram are equal. SO, ∠A=∠C and ∠B=∠D
So, ∠DAP=∠BCQ, AD=BC, ∠B=∠D
∴ By ASA congruency, AP=QC.
∴ APCQ is parallelogram and AP∥CQ.