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Another Condition for a Quadrilateral to Be a Parallelogram

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Theorem: A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.

In above fig. which is AB = CD and AB || CD .  Let us draw a diagonal AC. You can show that ∆ ABC ≅ ∆ CDA by SAS congruence rule. So ,  BC || AD . 

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Shaalaa.com | Theorem : A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.

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Theorem : A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. [00:12:07]
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