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Ex 8.1, 8 - ABCD is a rectangle in which diagonal AC bisects - Ex 8.1

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Ex 8.1, 8 ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: ABCD is a square Given: Rectangle ABCD where AC bisects ∠ A, i.e. ∠ 1 = ∠ 2 & AC bisects ∠ C, i.e. ∠ 3 = ∠ 4 To prove: ABCD is a square Proof: A square is a rectangle when all sides are equal Now, AD ∥ BC & AC as transversal ∠1 = ∠4 Now, ∠ 1 = ∠ 2 & ∠ 1 = ∠ 4 Hence, ∠ 2 = ∠ 4 In ∆ABC, ∠2 = ∠4 So, BC = AB But BC = AD & AB = DC From (1) & (2) ∴ AB = BC = CD = DA So, ABCD is a rectangle with all sides equal Hence, ABCD is a square. Ex 8.1, 8 ABCD is a rectangle in which diagonal AC bisects ∠ A as well as ∠ C. Show that: (ii) diagonal BD bisects ∠ B as well as ∠ D. In previous part we proved, ABCD is a square And diagonals of a square bisects its angles So, Diagonal BD bisects ∠B & ∠D. Hence proved

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