Given: Rectangle ABCD, CF ⟂ BD

Prove: AD / EC = AB / ED

Definition
AD / EC = AB / ED
ABCD is a parallelogram
Given
Definition
△DAB ~ △CED
AB ǁ CD
∠A is a right angle
Definition
AA similarity
∠ABD = ∠CDE
Rectangle ABCD, CF ⟂ BD
Perpendicular lines form right angles
∠DEC = ∠A
Parallel lines form equal alternate interior angles
∠DEC is a right angle
All right angles are equal
All rectangles are parallelograms