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Theorem 8.5 - Class 9 - If both pair of opposite angles are equal.jpg

Theorem 8.5 - Chapter 8 Class 9 Quadrilaterals - Part 2
Theorem 8.5 - Chapter 8 Class 9 Quadrilaterals - Part 3

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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.