Given: Rectangle ABCD, CF ⟂ BD

Prove: AD / EC = AB / ED

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