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

Example 1 - Chapter 8 Class 9 Quadrilaterals - Part 2

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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 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.