Answer:
AE = CF .
Why?
BD acts as a shape bisector because it cuts the entire rectangle in half from points B and D.
Given that AE is perpendicular to BD, and CF is perpendicular to BD (which we know BD is a bisector), that means that both AE and CF are of equal length inside the rectangle.
Another way to look at it is:
AE = CF because they are technically just vertical angles, shifted and displaced in a weird way; it is a different representation of vertical angles, only distorted. (Don't use this as your answer though, it needs more context. I just want to make it look easier to comprehend.)
