Problem

In quadrilateral \(EFGH\), opposite sides \(EF\) and \(GH\) are \(\text{both}~\text{parallel}~\text{and}~\text{congruent}\). Name the converse theorem that turns this \(\text{single}~\text{paired}~\text{condition}\) into the conclusion that \(EFGH\) is a parallelogram.

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Use the converse theorem: if both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram.

Use the converse theorem: if one pair of opposite sides of a quadrilateral is both parallel and congruent, then it is a parallelogram.

Use the converse theorem that diagonals bisecting each other imply a parallelogram.

Use the theorem that if one pair of opposite sides is parallel, then the quadrilateral is a parallelogram.

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