9) Prove that a quadrilateral is a parallelogram if a pair of opposite

1.	9) Prove that a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.
Answer» ong>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.

9) Prove that a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.

Answer»

ong>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.

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

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9) Prove that a quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.