Theorem 8.3 - Class 9 - If both pair of opposite sides are equal.jpg

2 Theorem 8.3 - Class 9 - Lines are Parallel i.e. AB CD.jpg
3 Theorem 8.3 - Class 9 - Both Pairs of Opposite sides are Parallel .jpg

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

Theorem 8.3 If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram. Given : ABCD is a quadrilateral, where AB = CD & AD = BC To Prove : ABCD is a Parallelogram. Construction : Join AC, AC is the diagonal Proof: In Δ ABC & Δ CDA AB = CD BC = DA AC = CA ∴ Δ ABC ≅ Δ CDA ∴ Δ ABC ≅ Δ CDA Hence, ∠ BAC = ∠DCA ∠ BCA = ∠DAC Thus, In ABCD, Both pairs of opposite sides are parallel, ∴ ABCD is a parallelogram

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