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Theorem 6.9 - Class 10 - If square of one side is equal to sum of

Theorem 6.9 - Chapter 6 Class 10 Triangles - Part 2
Theorem 6.9 - Chapter 6 Class 10 Triangles - Part 3


Transcript

Theorem 6.9: In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle. Given: A triangle ABC in which 〖𝐴𝐢〗^2=〖𝐴𝐡〗^2+〖𝐡𝐢〗^2 To Prove: ∠B=90Β° Construction: Draw Ξ” PQR right angled at Q, such that PQ = AB and QR = BC. Proof: In βˆ†PQR ∠Q=90Β° By Pythagoras theorem, 〖𝑃𝑅〗^2=〖𝑃𝑄〗^2+〖𝑄𝑅〗^2 Since PQ = AB and QR = BC 〖𝑃𝑅〗^2=〖𝐴𝐡〗^2+〖𝐡𝐢〗^2 Also, given that 〖𝐴𝐢〗^2=〖𝐴𝐡〗^2+〖𝐡𝐢〗^2 From (1) & (2) 〖𝑃𝑅〗^2=〖𝐴𝐢〗^2 PR = AC In Ξ” ABC & Ξ” PQR AC = PR AB = PQ BC = QR ∴ Ξ” ABC β‰… Ξ” PQR β‡’ ∠ B = ∠ Q Since ∠ Q = 90Β° ∴ ∠ B = 90Β° Hence Proved.

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Davneet Singh

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.