Because AB//CD

So angle ABD= angle CDB.

And because AE is perpendicular to BD, CF is perpendicular to BD.

So AEB angle CFD angle =90 degrees.

In triangle AEB and triangle CFD.

Angle ABD= angle CDB

Angle AEB= angle CFD=90 degrees

AE=CF

So the triangle AEB is equal to the triangle CFD.

So AB=CD