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Ex 8.2, 5 - In a parallelogram ABCD, E and F are mid-points - Ex 8.2

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Ex 8.2, 5 In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD. Given: ABCD is a parallelogram where E and F are the mid-points of sides AB and CD respectively To prove: AF & EC trisect BD i.e. BQ = QP = DP Proof: ABCD is a parallelogram. ∴ AB ∥ CD ⇒ AE ∥ CF & AB = CD 1/2 AB = 1/2 CD ∴ AE = CF In AECF, AE ∥ CF & AE = CF one pair of opposites sides is equal and parallel ∴ AECF is a parallelogram ⇒ AF ∥ CE ∴ PF ∥ CQ & AP ∥ EQ In ΔDQC, F is the mid-point of DC and PF ∥ CQ . ∴ P is the mid-point of DQ. ⇒ PQ = DP From (1) & (2) DP = PQ = BQ Hence, the line segments AF and EC trisect the diagonal BD. Hence proved

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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.
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