In parallelogram ABCD, M is the midpoint of AB, N is the midpoint of DC.
∴ AM = MB, DN = NC
In parallelogram ABCD, AB = CD
AB2=CD2=AM=DN
∴ AM = BM = DN = NC .....(i)
DM and BN are parallel lines.
Draw 2 lines through A & C parallel to DM.
From (1), these parallel lines are equidistant.
Thus, parallel lines DM & BN divide AC into 3 equal parts.
AP = PQ = QC