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If the diagonals of a quadrilateral bisect each other then what quadrilateral must be a parallelogram?
diagonals.
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.
What is the Opposite Sides Parallel and Congruent Theorem?
The Opposite Sides Parallel and Congruent Theorem states that if a quadrilateral has a pair of opposite sides that are parallel and congruent, then the quadrilateral is a parallelogram.
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.
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
What quadrilateral does not always have congruent diagonals?
A quadrilateral that does not always have congruent diagonals is a trapezoid. In a trapezoid, which has at least one pair of parallel sides, the diagonals are generally not congruent unless it is an isosceles trapezoid. Other types of trapezoids can have diagonals of different lengths. Thus, congruent diagonals are not a defining characteristic of all trapezoids.
The diagonals are congruent but the quadrilateral has no right angles is it a parallelogram?
No, a quadrilateral with congruent diagonals but no right angles is not necessarily a parallelogram. In order for a quadrilateral to be classified as a parallelogram, it must have both pairs of opposite sides parallel. The property of having congruent diagonals does not guarantee that the sides are parallel, so the quadrilateral may not be a parallelogram.
What quadrilateral had opposite sides parallel and all sides congruent?
A square's opposite sides are parallel and all the sides are congruent.
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
What is a quadrilateral with opposite sides parallel and congruent?
trapezoid
If one pair of opposite sides of a quadrilateral is parallel and then the quadrilateral is a parallelogram?
Then, the opposite sides are congruent.
What is a quadrilateral whose opposite sides are parallel and congruent and whose opposite angles are congruent?
its a shape
