P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD .prove that CQ is parallel to ac and also that ac bisects pq

Question

BD IS THE DIAGONAL AND DRAW AC A DIAGONAL 

BP + PQ+DP =BD

Answer 1

Using properties of parallelograms, prove

ΔAPD ≅ ΔCBQ   then

∠APB ≅ ∠CQB    by corresponding parts

AP || CQ            by alternate exterior angles

 

AC bisects DB    diagonals mutually bisect

Label intersection E

DE = BE             definition of bisect

DE = DP + PE     segments addition

BE = BQ + QE    segments addition

DP + PE = BQ + QE   substitution

DP = BQ             given as trisection

PE = QE             segment addition/subtraction