Question

prove that if a pair of opposite sides of a quadrilateral are equal and parallel, it is a parallelogram​

Answer 1

PLZ REFER WITH THE ATTATCHMENT.......

Answer 2

Given:-

A quadrilateral ABCD in which AB ║ DC and AB = DC.

To prove:-

ABCD is a parallelogram i.e., AB ║ DC and AD ║ BC.

Construction:-

Join A and C

Proof:-

$\sf Since \:AB ║ DC\: and\: AC\: is\: transversal$

∠BAC = ∠DCA [Alternate angles]

AB = DC [Given]

AC = AC [Common side]

$\sf\to ∆BAC ≅ ∆DCA [By \:SAS]$

Therefore, ∠BCA = ∠DAC [By cpctc]

But these are alternate angles and whenever alternate angles are equal, the lines are parallel.

AD ║ BC

AB ║ DC (given)

ABCD is a parallelogram .