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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
Are the diagonals of a quadrilateral both perpendicular and congruent?
In general, no, they are not.
If one side of a quadrilateral is congruent to its opposite side then the quadrilateral is a parallelogram?
No, it doesn't have to be. A quadrilateral can definitely be a parallelogram only if: - Both pairs of opposite sides are parallel. - Both pairs of opposite sides are congruent. - One pair of opposite sides are both congruent and parallel. - Both pairs of opposite angles are congruent. - The diagonals bisect each other.
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.
What do you call a quadrilateral having both pairs of opposite angles congruent?
A parallelogram.
What do you call a quadrilateral having both pairs of opposite sides congruent?
A parallelogram.
If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is not a parallelogram?
False. If both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram.
What are the proofs that a quadrilateral ia s parallelogram?
There are 5 ways to prove a Quadrilateral is a Parallelogram. -Prove both pairs of opposite sides congruent -Prove both pairs of opposite sides parallel -Prove one pair of opposite sides both congruent and parallel -Prove both pairs of opposite angles are congruent -Prove that the diagonals bisect each other
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 diagonals of a quadrilateral bisect each other when is the quadrilateral a parallelogram?
always
What is one way to prove that a quadrilateral is a parallegram?
* both pairs of opposite sides are parallel * both pairs of opposite sides are congruent * both pairs of opposite angles are congruent * one pair of opposite sides are parallel and congruent * both diagonals bisect each other * all consecutive angle pairs are supplementary
