Quadrilateral With One Opposite Pair Of Side Equal and Parallel is a Parallelogram
Quadrilateral With One Opposite Pair Of Side Equal and Parallel is a Parallelogram
Quadrilateral With One Opposite Pair of Side Equal and Parallel is a Parallelogram:
Theorem: A quadrilateral is a parallelogram, if its one pair of opposite sides are equal and parallel
Given: A quadrilateral ABCD such that AB = CD and AB || CD. To Prove: ABCD is a parallelogram Construction: Join AC Proof: In AB = CD [Given] AC = CA [Common]
But they are Alternate angles when BC and AD are straight lines and AC is the transversal, as they are equal so BC || AD Now both the opposite pair of sides are parallel So, ABCD is a parallelogram |  |
| Illustration: In a triangle ABC median AO is extended to D such that AO = OD. Prove that BACD is a parallelogram | |
Solution: In BO = OC [ AO is the median] AO = OD [Given]
But they are Alternate angles when AB and CD are straight lines and BC is the transversal, as they are equal so AB || CD. Now AB = CD and AB || CD, Therefore BACD is a parallelogram as its one pair of opposite sides are equal and parallel |  |
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