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Example 1 - Show that each angle of rectangle is right angle - Opposite angles of parallelogram

  1. Chapter 8 Class 9 Quadrilaterals
  2. Serial order wise
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Example 1 Show that each angle of a rectangle is a right angle. Given: A rectangle ABCD To prove: ∠ A = ∠ B = ∠ C = ∠ D = 90° Proof: We know that Rectangle is a parallelogram where one angle is 90°. Hence, lets assume ∠ A=90° Now, AD ∥ BC & AB is a transversal So, ∠ A + ∠ B = 180° ∠ B + 90° = 180° ∠ B = 180° – 90° ∠ B = 90° Now, we know that opposite angles of parallelogram are equal ∴ ∠ C = ∠ A and ∠ D = ∠ B ∴ ∠ C = 90° and ∠ D = 90°. So , each of the angles of a rectangle is a right angle. Hence proved

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Davneet Singh
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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