Theorem 8.5
If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
Given : ABCD is a quadrilateral
with opposite angles equal,
i.e. 1 = 3 & 2 = 4
To Prove : ABCD is a Parallelogram
Proof : By angle sum property of quadrilateral
1 + 2 + 3 + 4 = 360
1 + 2 + 1 + 2 = 360
2( 1 + 2) = 360
1 + 2 = 360 2
1 + 2 = 180
Similarly we can prove that,
1 + 4 = 180
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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