ABCD is a Parallelogram in which AP bisector angle A and BQ bisect angle B. Prove that AQ=BP , PQ= CD. ABPQ is a parallelogram, SELINA class 9 math ex 14 C question 4

ABCD is a Parallelogram in which AP bisector angle A and BQ bisect angle B. 

Prove that (i)AQ=BP 

                  (ii) PQ= CD

                                              (iii) ABPQ is a parallelogram

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In parallelogram ABCD, P is mid-point of AB. CP and BD intersect each other at point O. If area of POB = 40 cm^2, and OP : OC = 1:2, find: (i) Areas of BOC and PBC (ii) Areas of ABC and parallelogram ABCD.