Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Test the opposite-angles converse for a parallelogram
Problem
Decide whether the stated angle evidence is sufficient to prove a parallelogram: quadrilateral \(ABCD\) with \(\angle~A\cong~\angle~C\) and \(\angle~B\cong~\angle~D\).
A converse test requires the full hypothesis, so one matching angle pair cannot settle the classification. We’ll use cyclic vertex order to pair first with third and second with fourth, verify both opposite congruences, and only then apply the angle-based converse.
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