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
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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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