Theorem 6.8 (Pythagoras Theorem) - if right trinagle, the sqiare of the hypotenuseis equal to i.jpg

2 Adding 1 and 2 AD AC + CD AC = AB2 + BC2 Hence proved.jpg

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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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 :- ∆ABC right angle at B To Prove :- 𝐴𝐶﷮2﷯= 𝐴𝐵﷮2﷯+ 𝐵𝐶﷮2﷯ Construction :- Draw BD ⊥ AC Proof :- Since BD ⊥ 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. Adding (1) and (2) AD . AC + CD . AC = 𝐴𝐵﷮2﷯ + 𝐵𝐶﷮2﷯ AC (AD + CD) = 𝐴𝐵﷮2﷯ + 𝐵𝐶﷮2﷯ AC × AC = 𝐴𝐵﷮2﷯ + 𝐵𝐶﷮2﷯ AC2 = 𝐴𝐵﷮2﷯ + 𝐵𝐶﷮2﷯ Hence Proved

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