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