Given: Rectangle ABCD, CF ⟂ BD

Prove: AD / EC = AB / ED

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