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Theorem A:

A quadrilateral is a parallelogram if its opposite sides are congruent.

Theorem B:

A quadrilateral is a parallelogram if a pair of opposite sides is parallel and congruent.

Theorem C:

A quadrilateral is a parallelogram if its diagonals bisect each other.

Theorem D:

A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

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Q: Conditions which guarantee that a quadrilateral is a parallelogram?

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None of the conditions on the list that accompanies the question guarantees that a quadrilateral is a parallelogram. But then, none of them prevents it either.

False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.

False

A parallelogram must have 4 sides and so it must be a quadrilateral. However, the sides of a quadrilateral need not be parallel so a quadrilateral need not be a parallelogram.

A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.

Related questions

None of the conditions on the list that accompanies the question guarantees that a quadrilateral is a parallelogram. But then, none of them prevents it either.

"It has four sides" is a description that does not guarantee that a quadrilateral is a square.

False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.

False

false

no

A parallelogram must have 4 sides and so it must be a quadrilateral. However, the sides of a quadrilateral need not be parallel so a quadrilateral need not be a parallelogram.

A shape that is a parallelogram but not a quadrilateral doesn't exist.

No. A parallelogram is a special kind of quadrilateral.

A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.

No. It is false. If both of those conditions are met, then the quadrilateral is a square.

In this case, the quadrilateral is sometimes a parallelogram.

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