Question

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

Answer 1

Answer:

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

Answer:

Hence proved.

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.