Question

Prove that "A quadrilateral is a parallelogram, if it's one pair of opposite sides are equal and parallel."​

Answer 1

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Answer 2

To prove △ABCD is a parallelogram.

Construction : Join AC

PROOF:

In △ABC and CDA, we have

AB = DC

AC = AC

and Angle BAC = Angle DCA

so by SAS congruence rule, we have

△ABC = △CDA

=> Angle BCA = angle DAC

Thus, line ac intersects AB and DC at A and C respectively such that

Angle DAC = Angle BCA

i.e, alternate interior angles are equal.

AD || BC

Thus, AB || CD and AD || BC.

Hence, Quadrilateral ABCD is a parallelogram.