InterviewSolution
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InterviewSolution
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termProve that in a right angled triangle square of the hypotenuse is equal to sum of the squaresof other two sides.425.ilar to AABC |
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Answer» Given:A ∆ XYZ in which ∠XYZ = 90°. To prove:XZ2= XY2+ YZ2Construction:Draw YO ⊥ XZProof:In ∆XOY and ∆XYZ, we have,∠X = ∠X → common∠XOY = ∠XYZ → each equal to 90°Therefore, ∆ XOY ~ ∆ XYZ → by AA-similarity⇒XO/XY = XY/XZ⇒ XO × XZ = XY2----------------- (i)In ∆YOZ and ∆XYZ, we have,∠Z = ∠Z → common∠YOZ = ∠XYZ → each equal to 90°Therefore, ∆ YOZ ~ ∆ XYZ → by AA-similarity⇒ OZ/YZ = YZ/XZ⇒ OZ × XZ = YZ2----------------- (ii) From (i) and (ii) we get, XO × XZ + OZ × XZ = (XY2+ YZ2) ⇒ (XO + OZ) × XZ = (XY2+ YZ2) ⇒ XZ × XZ = (XY2+ YZ2) ⇒ XZ2= (XY2+ YZ2) |
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