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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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