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Which description does NOT guarantee that a quadrilateral is a parallelogram?

A.
a quadrilateral with both pairs of opposite sides congruent

B.
a quadrilateral with the diagonals bisecting each other

C.
a quadrilateral with consecutive angles supplementary

D.
a quadrilateral with two opposite sides parallel

1 Answer

1 vote

Final answer:

The description that does NOT guarantee that a quadrilateral is a parallelogram is: a quadrilateral with two opposite sides parallel.

Step-by-step explanation:

A quadrilateral is a parallelogram if it satisfies certain conditions. Let's go through each description to determine which one does not guarantee that a quadrilateral is a parallelogram:

A. A quadrilateral with both pairs of opposite sides congruent - This condition is true for parallelograms, so it guarantees that a quadrilateral is a parallelogram.

B. A quadrilateral with the diagonals bisecting each other - This condition is true for parallelograms, so it guarantees that a quadrilateral is a parallelogram.

C. A quadrilateral with consecutive angles supplementary - This condition is true for parallelograms, so it guarantees that a quadrilateral is a parallelogram.

D. A quadrilateral with two opposite sides parallel - This condition is required for a quadrilateral to be a parallelogram, but it is not sufficient. It is possible for a quadrilateral to have two opposite sides parallel and still not be a parallelogram (e.g., a trapezoid).

Therefore, the correct answer is option D: a quadrilateral with two opposite sides parallel.

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