Subjects geometry

Parallelogram Error 8Ed255

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1. **State the problem:** Ahmed recalls a theorem that states if one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. He tries to prove a figure is a parallelogram by stating it has a pair of opposite sides congruent and a pair of opposite sides parallel, but not necessarily the same pair. 2. **Recall the theorem:** The theorem says: *If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.* This means the **same** pair of opposite sides must be both congruent and parallel. 3. **Analyze Ahmed's error:** Ahmed's explanation says one pair of opposite sides is congruent and a (possibly different) pair of opposite sides is parallel. This does not satisfy the theorem because the congruent and parallel sides must be the same pair. 4. **Conclusion:** The error is that Ahmed did not ensure the same pair of opposite sides is both congruent and parallel. 5. **Answer:** The correct choice is: **A. In order to apply the theorem, the same pair of opposite sides must be both parallel and congruent.**