Ex 7.2, 6 - ABC is an isosceles triangle in which AB = AC - Opposite Angles of equal sides

Ex 7.2, 6 - Chapter 7 Class 9 Triangles - Part 2

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Ex 7.2, 6 ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠BCD is a right angle. Given: AB = AC Also, AD = AB i.e. AC = AB = AD To prove: ∠BCD = 90° Proof: In ΔABC, AB = AC ⇒ ∠ACB = ∠ABC In ΔACD, AC = AD ∠ADC = ∠ACD In ΔBCD, ∠ABC + ∠BCD + ∠BDC = 180° ∠ACB + ∠ BCD + ∠ACD = 180° (∠ACB +∠ACD) + ∠ BCD = 180° (∠ BCD) + ∠ BCD = 180° 2∠ BCD = 180° ∠ BCD = (180°)/2 ∠ BCD = 90° Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.