Theorem 8.5 - Chapter 8 Class 9 Quadrilaterals

Last updated at Dec. 16, 2024 by

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

part 2 - Theorem 8.5 - Theorems - Serial order wise - Chapter 8 Class 9 Quadrilaterals
part 3 - Theorem 8.5 - Theorems - Serial order wise - Chapter 8 Class 9 Quadrilaterals

 

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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 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 and Computer Science at Teachoo