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

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.