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The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.

Q: Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?

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False

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

A quadrilateral is a parallelogram if and only if its diagonals bisect each other (this should be in any geometry book)

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.

No.

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always

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The missing word is "bisect".

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diagonals.

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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.

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Parallelogram and rhombus.