1 Theorem 6.9- In a triangle, if one side is equal to the sum.JPG

2 Theorem 6.9- In PQR, By pythagoras theorem.JPG
3 Theorem 6.9-Now in ABC and PQR.JPG

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Transcript

Theorem 6.9 :- In a right 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 2 = 2 + 2 To Prove :- B=90 Construction :- Draw PQR right angled at Q, such that PQ = AB and QR = BC. Proof :- In PQR Q=90 By Pythagoras theorem, 2 = 2 + 2 Since PQ = AB and QR = BC 2 = 2 + 2 Also, given that 2 = 2 + 2 From (1) & (2) 2 = 2 PR = AC Now, In ABC & PQR AC = PR AB = PQ BC = QR ABC PQR B = Q Since Q = 90 B = 90 Hence Proved.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.