InterviewSolution
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InterviewSolution
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Prove that in a right angled triangle square of the hypotenuse is equal to sum of the squaresof other two sides.25.4 |
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Answer» Given: A right angled ∆ABC, right angled at B To Prove- AC²=AB²+BC² Construction: draw perpendicular BD onto the side AC . Proof: We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other. We have △ADB∼△ABC. (by AA similarity) Therefore, AD/ AB=AB/AC (In similar Triangles corresponding sides are proportional) AB²=AD×AC……..(1) Also, △BDC∼△ABC Therefore, CD/BC=BC/AC (in similar Triangles corresponding sides are proportional) Or, BC²=CD×AC……..(2) Adding the equations (1) and (2) we get, AB²+BC²=AD×AC+CD×AC AB²+BC²=AC(AD+CD) ( From the figure AD + CD = AC) AB²+BC²=AC . AC Therefore, AC²=AB²+BC² This theroem is known as Pythagoras theroem. |
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