Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Complete a parallelogram proof by choosing the missing converse theorem
Problem
In quadrilateral \(ABCD\), \(AB~=~CD\) and \(BC~=~AD\). Name the converse theorem that turns these \(\text{two}~\text{pairs}~\text{of}~\text{congruent}~\text{opposite}~\text{sides}\) into the conclusion that \(ABCD\) is a parallelogram.
A proof cannot use a property of an already-known parallelogram when the parallelogram classification is what must be proved. We’ll translate both given equalities into opposite-side congruences, check that the two required pairs are complete, and use the statement whose implication runs from that evidence to the desired classification.
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