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Q: The diagonals of a quadrilateral must bisect each other and be perpendicular to guarantee that the quadrilateral is a parallelogram?

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False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.

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.

True. Only if the given angle is between the two sides will the two triangles guarantee to be congruent (SAS), unless the given angle is a right angle (90°) in which case you now have RHS (Right-angle, Hypotenuse, Side) which does guarantee congruence.

No congruent sides or No congruent angles --Algebra 2 Teacher

Related questions

False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.

"It has four sides" is a description that does not guarantee that a quadrilateral is a square.

false

no

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.

A quadrilateral is not necessarily a rectangle. The only time this is not true is in the case of a square on a quadrilateral without four 90 degree angles.

QR=5,ST=5 QT is paralellel to RS

I can guarantee you that. Indeed you can use guarantee in a sentence.

guarantee

A guarantee provided by a corporation, a legal person, is known is corporate guarantee.

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