Theorem 8.7 - If diagonals bisect each other, then it is parallelogram.jpg

2 Theorem 8.7 - Lines are Parallel i.e AB CD.jpg
3 Both pairs of opposite.jpg

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Theorem 8.7 If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. Given: ABCD is a quadrilateral with AC and BD are diagonals intersecting at O Diagonals bisect each other i.e. OA = OC & OB = OD To Prove: ABCD is a parallelogram Proof : In ∆AOD and ∆COB OA = OC ∠AOD = ∠COB OD = OB △ AOD ≅ △COB △ ODA ≅ △OBC ∴ ∠OAD = ∠OCB Similarly, we can prove △ AOB ≅ △COD ∴ ∠ABO = ∠CDO Thus, In ABCD, Both pairs of opposite sides are parallel, ∴ ABCD is a parallelogram

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