#### theorem

**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.

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

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