Question

A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel,prove it please quickly

Answer 1

Answer:

Step-by-step explanation:

Given: ABCD is quadrilateral and AB║CD, AB=CD.

To prove: ABCD is a parallelogram

Proof: AC is a transversal and also AB║CD, therefore

∠BAC=∠DCA(Alternate angles)

In ΔADC and ΔCBA, we have

AB=CD(Given)

∠BAC=∠DCA(Alternate angles)

AC=CA(Common)

ΔADC≅ΔCBA by the SAS rule.

Hence, by CPCT, DA=BC

Thus, Both the pair of opposite sides are equal in the quadrilateral ABCD, therefore ABCD is a parallelogram.

Hence proved.

Answer 2

Full explanation

Given: ABCD is quadrilateral and AB║CD, AB=CD.

To prove: ABCD is a parallelogram

Proof: AC is a transversal and also AB║CD, therefore

∠BAC=∠DCA(Alternate angles)

In ΔADC and ΔCBA, we have

AB=CD(Given)

∠BAC=∠DCA(Alternate angles)

AC=CA(Common)

ΔADC≅ΔCBA by the SAS rule.

Hence, by CPCT, DA=BC

Thus, Both the pair of opposite sides are equal in the quadrilateral ABCD, therefore ABCD is a parallelogram.

Hence proved.

Thanks

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