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Theorem 8.5 - Class 9th - If both pair of opposite angles are equal, then it is a parallelogram - Opposite angles of parallelogram

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  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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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 is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
  • Devansh Tanwar's image
    Devansh Tanwar
    Nov. 12, 2017, 8 p.m.
    Can't we prove theorem 8.5 using theorem 8.1 that states ' diagonal of a paralleogram divides it into two congruent triangles" ? 
    I meant to say : 
    1.Draw the diagonal
    2.Based on given data, prove that 2 triangles are congruent. 
    3.Atlast say " as the diagonal divides the given figure into two congruent triangles it is a paralleogram."
    Is my method correct??
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  • Vikas Dixit Vikas Dixit's image
    Vikas Dixit Vikas Dixit
    Aug. 20, 2017, 7:41 p.m.
    Transversal

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  • Ibhrahim Uddin's image

    can you please list out some important questions or parts in the sa-2 portion of mathematics grade9

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  • Nataraj Matta's image
    My my quadrilateral chapter theorems are not working circle theorems are coming in quadrilateral theorem please correct this
    View answer
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