Last updated at May 29, 2018 by Teachoo

Transcript

Theorem 8.3 If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given : ABCD is a quadrilateral, where AB = CD & AD = BC To Prove : ABCD is a Parallelogram. Construction : Join AC, AC is the diagonal Proof: In Δ ABC & Δ CDA AB = CD BC = DA AC = CA ∴ Δ ABC ≅ Δ CDA ∴ Δ ABC ≅ Δ CDA Hence, ∠ BAC = ∠DCA ∠ BCA = ∠DAC Thus, In ABCD, Both pairs of opposite sides are parallel, ∴ ABCD is a parallelogram

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.