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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

 


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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.