 ##### Asked by: Yenny Afan De Rivera
asked in category: General Last Updated: 11th June, 2020

# What theorem or postulate is used to prove ABCD is a parallelogram?

Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem: Opposite angles of a parallelogram are congruent to each other.

People also ask, how do you prove that ABCD is a parallelogram?

triangles are congruent. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then ABCD is a parallelogram. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Similarly, how do you prove it is a parallelogram? To prove a quadrilateral is a parallelogram, you must use one of these five ways.

1. Prove that both pairs of opposite sides are parallel.
2. Prove that both pairs of opposite sides are congruent.
3. Prove that one pair of opposite sides is both congruent and parallel.
4. Prove that the diagonals bisect each other.

Also to know is, what statement is used to prove that quadrilateral ABCD is a parallelogram?

Answer: Opposite sides must be congruent. We have to prove that this is a parallelogram.

What theorems prove a quadrilateral is a parallelogram?

THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram. THEOREM: If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram. THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.

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11th June, 2020

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