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Properties of a Parallelogram - Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.

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Theorem:  If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
Proof: Let sides AB and CD of the quadrilateral ABCD be equal and also  AD = BC in following fig.

Draw diagonal AC. Clearly, ∆ ABC ≅ ∆ CDA 
So, ∠ BAC = ∠ DCA 
and ∠ BCA = ∠ DAC
Hence ABCD is a parallelogram.

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Shaalaa.com | Theorem: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

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Theorem: If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. [00:03:52]
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