Dear Student!

Here is the answer to your query.

Given : ABCD and BCEF are two parallelograms with same base BC 

To prove : AE || BC

Proof : We know that area of parallelogram = base × height

also given that area (parallelogram ABCD) = Area (Parallelogram BCEF)

⇒ BC × height of ABCD = BC × height of BCEF

⇒ Height of ABCD = Height of BCEF

Since the perpendicular distance of both the parallelogram are same 

 ∴ AE || BC

Hence we can conclude that parallelogram with same base and equal area lie between same parallel line.

Cheers!