Prove that .in a right triangle.the square on the hypotenuse is equal to the sum of the square on the other two side.
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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
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
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