Question 3 - Important questions of Triangle (in Geometry) - Chapter 6 Class 10 Triangles
Last updated at April 16, 2024 by Teachoo
Important questions of Triangle (in Geometry)
Important questions of Triangle (in Geometry)
Last updated at April 16, 2024 by Teachoo
Question 3 In Fig. 6.58, ABC is a triangle in which ABC > 90 and AD CB produced. Prove that AC2 = AB2 + BC2 + 2 BC . BD. Given : ABC is a triangle in which ABC > 90 and AD CB extended D. To Prove: AC2 = AB2 + BC2 + 2BC.BD Proof: In right ADB Applying Pythagoras theorem, AB2 = AD2 + BD2 In right ADC Applying Pythagoras theorem, AC2 = AD2 + CD2 From (2) AC2 = AD2 + CD2 AC2 = AD2 + (BD + BC)2 AC2 = AD2 + BD2 + BC2 + 2BD.BC Put AD2 + BD2 = AB2 from equation (1) AC2 = AB2 + BC2 + 2BC.BD. Hence Proved.