Q7. Show that a quadrilateral is a parallelogram if its opposite sides

1.	Q7. Show that a quadrilateral is a parallelogram if its opposite sides are equal.
Answer» ABCD is QUADRILATERAL and AB║CD, AB=CD.To prove: ABCD is a parallelogramProof: AC is a transversal and ALSO AB║CD, therefore∠BAC=∠DCA(Alternate ANGLES)In ΔADC and ΔCBA, we haveAB=CD(Given)∠BAC=∠DCA(Alternate angles)AC=CA(COMMON)ΔADC≅ΔCBA by the SAS rule.Hence, by CPCT, DA=BCThus, Both the pair of opposite SIDES are equal in the quadrilateral ABCD, therefore ABCD is a parallelogram.Hence proved.

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Q7. Show that a quadrilateral is a parallelogram if its opposite sides are equal.​

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Q7. Show that a quadrilateral is a parallelogram if its opposite sides are equal.