Given: Rectangle ABCD, CF ⟂ BD

Prove: AD / EC = AB / ED

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