Question

Prove with reason that if one pair of opposite sides of any quadrilateral is equal as well as parallel then the quadrilateral will be a parallelogram​

Answer 1

Prove:

Question

If each pair of opposite sides of a quadrilateral is equal the it is a parallelogram.

Given:- A quadrilateral ABCD in which AB=CD and AD=BC.

To prove:- AB∥CD and AD∥BC

Construction:- Joi A and C.

Proof:-

In △ABC and △CDA,

AB=CD(Given)

AD=BC(Given)

AC=AC(Common)

∴△ABC≅△CDA(By SSS)

Therefore, by CPCTC,

∠ACD=∠BAC

∠DAC=∠ACB

Since alternate anglea are equal, thus the ines are parallel.

Therefore,

AB∥CD and AD∥BC

Since both the pairs of opposite sides of quadrilateral are parallel, ABCD is a parallelogram.

Hence proved.

Step-by-step explanation:

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