Consider squares ABCD and PQRS.
∠A = ∠P, ∠B = ∠Q, ∠C = ∠R, ∠D = ∠S
$\frac{ AB }{ PQ }=\frac{ BC }{ QR }=\frac{ CD }{ RS }=\frac{ AD }{ PS }$
Case 2: The two quadrilaterals are of different types.
Consider square ABCD and rectangle STUV.
∠A = ∠S, ∠B = ∠T, ∠C = ∠U, ∠D = ∠V
Now, $\frac{ AB }{ ST }=\frac{ CD }{ UV }$ and $\frac{ BC }{ TU }=\frac{ AD }{ SV }$ But $\frac{ AB }{ ST } \neq \frac{ BC }{ TU }$
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