We know that
Area of △ ABD = ½ × AB × DL …….. (1)
Area of △ CBD = ½ × CD × BE …….. (2)
Hence, ABCD is a parallelogram.
It can be written as AB || CD and
AB = CD …… (3)
We know that the distance between two parallel lines is constant t,
So we get
DL = BE …….. (4)
Using the equations (1), (2), (3) and (4)
We get
Area of △ ABD = ½ × AB × DL
It can be written as
Area of △ ABD = ½ × CD × BE
So we get
Area of △ ABD = Area of △ CBD
Therefore, it is proved that a diagonal divides a parallelogram into two triangles of equal area.