Check sibling questions

Ex 3.1, 3 - What is the sum of angles of a convex quadrilateral?

Ex 3.1, 3 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 2
Ex 3.1, 3 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 3
Ex 3.1, 3 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 4

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Transcript

Ex 3.1, 3 What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!) Convex Quadrilateral In Quadrilateral ABCD Sum of Angles of ABCD = ∠ A + ∠ B + ∠ C + ∠ D Let’s divide Quadrilateral ABCD into two triangles – Δ ABC & Δ ADC Now, We know that Sum of angles of a triangle is 180° For Δ ABC ∠ BAC + ∠ B + ∠ BCA = 180° For Δ ADC ∠ DAC + ∠ D + ∠ DCA = 180° Adding (1) & (2) ∠ BAC + ∠ B + ∠ BCA + ∠ DAC + ∠ D + ∠ DCA = 180° + 180° (∠ BAC + ∠ DAC) + ∠ B + (∠ BCA + ∠ DCA) + ∠ D = 360° ∠ A + ∠ B + ∠ C + ∠ D =360° So, Sum of angles of convex quadrilateral = 360° Let’s try for non-convex quadrilateral Non-Convex Quadrilateral In Quadrilateral ABCD Sum of Angles of ABCD = ∠ A + ∠ B + ∠ C + ∠ D Let’s divide Quadrilateral ABCD into two triangles – Δ ABC & Δ ADC Now, We know that Sum of angles of a triangle is 180° For Δ ABC ∠ BAC + ∠ B + ∠ BCA = 180° For Δ ADC ∠ DAC + ∠ D + ∠ DCA = 180° Adding (1) & (2) ∠ BAC + ∠ B + ∠ BCA + ∠ DAC + ∠ D + ∠ DCA = 180° + 180° (∠ BAC + ∠ DAC) + ∠ B + (∠ BCA + ∠ DCA) + ∠ D = 360° ∠ A + ∠ B + ∠ C + ∠ D =360° So, Sum of angles of non-convex quadrilateral = 360° Hence, sum of angles is same for both convex and non-convex quadrilaterals.

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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.