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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.