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.
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.
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.
No. It is false. If both of those conditions are met, then the quadrilateral is a square.
A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral in which the opposite sides are parallel.
No. A parallelogram is a special kind of quadrilateral.
A shape that is a parallelogram but not a quadrilateral doesn't exist.
In this case, the quadrilateral is sometimes a parallelogram.