Question

prove that in a right triangle the square of the hypotenuse is equal to the sum of the square of the other two sides

Answer 1

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=90

to prove:AB2+BC2=AC2

proof: in triangle ABD and tri ABC,

angle A=angle A

angle ADB=angleBDC=90

therefore,triADB is similar to triABC.

which implies AD/AB=AB/AC (sides are in proportion)

which implies AD*AC=AB2-------1

IIIly, tri BDC is similar to tri ABC

BC/DC=AB/BC (sides are in proportion)

which implies AC*DC=BC2-----2

add 1 and 2

AD.AC=AB2

AD.AC+AC.DC=AB2+BC2

=AC(AD+DC)=AB2+BC2

=AC2=AB2+BC2

Hence proved.

Answer 2

refer to NCERT book class 10 chapter 6 triangles second last theorm