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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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โˆ™ 2010-10-11 10:48:36
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Q: Conditions which guarantee that a quadrilateral is a parallelogram?
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Related questions

Which of these conditions does not guarantee that a quadrilateral is a parallelogram?

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.


Which description does not guarantee that a quadrilateral is a square?

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


True or false the diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?

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


The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?

False


The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram.?

false


Is it true that The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?

no


Why is a parallelogram always a quadrilateral but a quadrilateral is only sometimes a parallelogram?

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.


What shape is a parallelogram but not a quadrilateral?

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


Is parallelogram and quadrilateral the same thing?

No. A parallelogram is a special kind of quadrilateral.


What is a quadrilateral parallelogram?

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


Is it true that the diagonals of a quadrilateral must bisect each other and be perpendicular to guaantee that the quadrilateral is a parallelogram?

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


If one diagonal of a quadrilateral bisects the other when is the quadrilateral a parallelogram?

In this case, the quadrilateral is sometimes a parallelogram.

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