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If both pairs of opposite sides are parallel: A Rectangle, or a Square.
If exactly one pair of opposite sides are parallel: An Isosceles Trapezoid.
If it does not have parallel sides and one diagonal is the perpendicular bisector of the other: A Kite
It is also possible that it does not have any parallel sides and neither diagonal is the perpendicular bisector of the other: A quadrilateral
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Conditions which guarantee that a quadrilateral is a parallelogram?
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.
In which parallelogram are the diagonals congruent?
If a parallelogram is in the form of a rectangle then both diagonals are congruent in lengths.
If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram?
always
A quadrilateral with both pairs of opposite sides congruent?
A quadrilateral with both pairs of opposite sides congruent is a parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent is the quadrilateral a parallelogram?
Yes
