Theorem 6.8 - Pythagoras Theorem Proof - Class 10 Chapter 6

Theorem 6.8 - Chapter 6 Class 10 Triangles - Part 2

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Theorem 6.8 (Pythagoras Theorem) : If a right triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides. Given: βˆ†ABC right angle at B To Prove: 〖𝐴𝐢〗^2= 〖𝐴𝐡〗^2+〖𝐡𝐢〗^2 Construction: Draw BD βŠ₯ AC Proof: Since BD βŠ₯ AC Using Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of the a right triangle to the hypotenuse then triangle on both side of the perpendicular are similar to whole triangle and to each other. Ξ” ADB ∼ Ξ” ABC Since, sides of similar triangles are in the same ratio, β‡’ 𝐴𝐷/𝐴𝐡= 𝐴𝐡/𝐴𝐢 β‡’AD . AC= 〖𝐴𝐡〗^2 Ξ” BDC ∼ Ξ” ABC Since, sides of similar triangles are in the same ratio β‡’ 𝐢𝐷/𝐡𝐢= 𝐡𝐢/𝐴𝐢 β‡’CD . AC= 〖𝐡𝐢〗^2 Adding (1) and (2) AD . AC + CD . AC = 〖𝐴𝐡〗^2 + 〖𝐡𝐢〗^2 AC (AD + CD) = 〖𝐴𝐡〗^2 + 〖𝐡𝐢〗^2 AC Γ— AC = 〖𝐴𝐡〗^2 + 〖𝐡𝐢〗^2 〖𝐴𝐢〗^2 = 〖𝐴𝐡〗^2 + 〖𝐡𝐢〗^2 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.