Question

show the diagonals of a parallelogram divide it four triangles of equal area.

Answer 1

proof : ABCD is a parallelogram
therefore OA = OC and  OB=OD ...(since diagonals of a parallelogram bisect each other)
Construction: Draw BE⊥AC 

now, area of OAB = OA * BE/2
and area of OBC = OC * BE/2

But OA=OC
therefore area of OAB = area of OBC
Similarly, area of OBC= area of OCD
Therefore, 
Area of OAB = area of OBC = area of OCD = area of ODA

Hence proved

To understand better draw a parallelogram with sides ABCD and diagonals AC and BD