Ex 3.3, 3 - Can a quadrilateral ABCD be a parallelogram if (i)

Ex 3.3, 3 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 2

 

  1. Chapter 3 Class 8 Understanding Quadrilaterals
  2. Serial order wise

Transcript

Ex 3.3, 3 Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°?Given a quadrilateral ABCD where ∠D + ∠B = 180° If ABCD is a parallelogram, then Opposite angles of a Parallelogram are equal ∴ ∠B = ∠D Given, ∠D + ∠B = 180° Putting ∠ D = ∠ B ∠B + ∠B = 180° 2∠B = 180° ∠ B = (180°)/2 ∠B = 90° ∴ ∠B = ∠D = 90° So, ABCD is a parallelogram where ∠B = ∠D = 90° which is possible only if ABCD is a square or a rectangle ∴ ABCD may be a parallelogram, But not in all cases.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.