1.

9) Prove that a quadrilateral is a parallelogram if a pair of opposite sides is equal andparallel.​

Answer»

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.


Discussion

No Comment Found

Related InterviewSolutions