##### 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?

**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.**

- Prove that both pairs of opposite sides are parallel.
- Prove that both pairs of opposite sides are congruent.
- Prove that one pair of opposite sides is both congruent and parallel.
- 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.