Question

Prove that if both pairs of opposite sides of a
quadrilateral are equal, then it is a parallelogram.
plz tell me the answer with step by step explanation.
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Answer 1

Given: A quadrilateral ABCD in which

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

Construction : Join A and C

Proof : In ∆ABC and ∆CDA

AB = DC [Given]

AD = BC [Given]

And AC = AC [Common]

∴ ∆ABC ≅ ∆CDA [By SSS]

⇒ ∠1 = ∠3 [By cpctc]

And ∠2 =∠4 [By cpctc]

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

∴ AB ║ DC and AD ║ BC

⇒ ABCD is a parallelogram.

Answer 2

Step-by-step explanation:

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