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Pythagores theorem |
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Answer» The sum of hypotenuse is equal to the sum of other two side of triangle is called pythagoras theorem. AC²=AB²+BC² \xa0Pythagoras TheoremStatement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.\xa0Given: A right triangle ABC right angled at B.To prove: AC2\xa0= AB2\xa0+ BC2Construction: Draw BD\xa0ACProof :We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.ADB\xa0ABCSo,\xa0(Sides are proportional)Or, AD.AC = AB2\xa0... (1)Also,\xa0BDC\xa0ABCSo,\xa0Or, CD. AC = BC2\xa0... (2)Adding (1) and (2),AD. AC + CD. AC = AB2\xa0+ BC2AC (AD + CD) = AB2\xa0+ BC2AC.AC = AB2\xa0+ BC2AC2\xa0= AB2\xa0+ BC2Hence Proved. Hypotenuse^2 = base ^ 2 + altitude ^ 2 |
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