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Example 13 - BL and CM are medians of a triangle ABC - Pythagoras Theoram - Proving

Example 13 - Chapter 6 Class 10 Triangles - Part 2
Example 13 - Chapter 6 Class 10 Triangles - Part 3


Transcript

Example 13 BL and CM are medians of a triangle ABC right angled at A. Prove that 4 (BL2 + CM2) = 5 BC2. Given: Δ ABC right angled at A ,i.e., ∠ 𝐴=90° Where BL and CM are the medians To Prove: 4(BL2 + CM2) = 5 BC2 Proof :- Since BL is the median, AL = CL = 1/2 AC Similarly, CM is the median AM = MB = 1/2 AB We know that, by Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 Now, (BC)2 = (AB)2 + (AC)2 …(1) 4BL2 = 4(AB)2 + AC2 …(2) 4 CM2 = AB2 + 4 AC2 …(3) Adding (2) and (3) 4 BL2 + 4CM2 = 4AB2 + AC2 + AB2 + 4AC2 4(BL2 + CM2) = 5AB2 + 5AC2 4(BL2 + CM2) = 5 (AB2 + AC2) 4(BL2 + CM2) = 5 BC2 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.