Prove that square of hypotenuse is square of other two sides

1.	Prove that square of hypotenuse is square of other two sides
Answer» statement:in a right triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.construct a right triange right angled at B.construction:construct a perpendicular BD on side AC.given:angleB=90to prove:AB2+BC2=AC2proof: in triangle ABD and tri ABC,angle A=angle Aangle ADB=angleBDC=90therefore,triADB is similar to triABC.which implies AD/AB=AB/AC (sides are in proportion)which implies ADAC=AB2-------1IIIly, tri BDC is similar to tri ABCBC/DC=AB/BC (sides are in proportion)which implies ACDC=BC2-----2add 1 and 2AD.AC=AB2AD.AC+AC.DC=AB2+BC2=AC(AD+DC)=AB2+BC2=AC2=AB2+BC2Hence proved. Please see theorm 6.8 in ncert mths book .

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