`P\ a n d\ Q` are the points of trisection of the diagonal `B D` of a parallelogram `A B C Ddot` Prove that `C Q` is parallel to `A Pdot` Prove also that `A C` bisects `P Q`.

Explanation

Since diagonals of a parallelogram bisect each other.
Therefore,`OA=OC \and\ OB=OD`
Since `P \and\ Q` are points of trisection of BD.
`BP=PQ=QD`
`OB=OD \and\ BP=QD`
`=>OP−BP=OD−QD`
`=>OP=OQ`
Thus, in quadrilateral APCQ, we have
`OA=OC \and\ OP=OQ`
Diagonals of quadrilateral APCQ bisect each other
`=>APCQ` is a parallelogram
Hence, `AP∥CQ`