Question

ABCD is a parallelogram diagonal AC and BD intersects at O. prove that the diagonals are bisectors of each other.

Answer 1

In Parellellogram opposite sides are equal.
Consider triangle AOB and triangle DOC

AB = DC ( Opposite sides of parellelogram are equal )
Angle OAB = Angle OCD ( Interior opposite angles are equal for parellogram)
Angle ABO = Angle ODC ( Interior opposite angles are equal for parellogram)

Therefore triable AOB is congruent to triangle DOC (as per ASA rule )
Therefore BO = OD and AO = OC.
Therefore the diagonals are bisectors of each other