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Ex 8.1, 2 - If diagonals of a parallelogram are equal - Ex 8.1

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Ex 8.1, 2 If the diagonals of a parallelogram are equal, then show that it is a rectangle. Given: Let ABCD be a parallelogram where AC = BD To prove: ABCD is a rectangle Proof: Rectangle is a parallelogram with one angle 90° We prove that one of its interior angles is 90°. In ΔABC and ΔDCB, AB = DC BC = BC AC = DB ∴ ΔABC ≅ ΔDCB ⇒ ∠ABC = ∠DCB Now, AB ∥ DC & BC is a transversal ∴ ∠B + ∠C= 180° ∠B + ∠B = 180° 2∠B = 180° ∠B = "180°" /"2" = 90° So, ABCD is a parallelogram with one angle 90° ∴ ABCD is a rectangle

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