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

2 Theorem 8.5 - Since interior angles on same side of transversal are supplementary.jpg
3 Theorem 8.5 - Both pairs of Opposite sides are Parallel ABCD is Parallelogram.jpg

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise

Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.