# Theorem 8.8

Last updated at April 19, 2017 by Teachoo

Last updated at April 19, 2017 by Teachoo

Transcript

Theorem 8.8 A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel. Given : ABCD is a quadrilateral where AB ∥ CD & AB = CD To Prove : ABCD is a Parallelogram Proof : Given AB ∥ CD with transversal AC. ∠BAC = ∠DCA In Δ ADC & Δ CBA AB = CD ∠BAC = ∠DCA AC = CA ∴ Δ ADC ≅ Δ CBA Hence, DA = BC Thus, In ABCD, Both pairs of opposite sides are equal ∴ ABCD is a Parallelogram. Hence proved

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.