Given, a quadrilateral ABCD with AB = DC and DO = OB.

**To prove:** ABCD a parallelogram

**Construction:** Draw OX DC.

In Î” BCD,

O is the mid point of BD and OX DC.

âˆ´By converse of mid point theorem,

X is the mid point of BC and OX = DC.

As AB = DC

âˆ´ OX = AB.

Now, in Î” ABC,

X is the mid point of BC and OX = AB.

âˆ´ By converse of mid point theorem,

O is the mid point of AC and OX AB

As OX AB and OX DC

â‡’ AB DC

Now, AB DC and AB = DC

âˆ´ ABCD is a parallelogram.

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