Question

understand the pythagores theorem and proof

Answer 1

The theorem which is used for measuring sides of only a particular triangle, that is, right angled triangle.

Theorem:
(Hypotenuse)^2= (Perpendicular)^2 + (Base)^2

Answer 2

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In a right right triangle the square of hypotenuse is equal to the sum of square of other 2 sides

Given:-
A right angle triangle ABC right angled
at B
to prove that:-

${ac}^{2} = {ab}^{2} + {bc}^{2}$
construction:- Draw BD perpendicular AC

proof:- consider a triangle ADB & ABC

$\frac{ad}{ab} = \frac{ab}{ac}$
${ab}^{2} = ad \times ac \: \: \: \: \: \: equation \: (1)$
consider triangle ABC & ABC

$\frac{cd}{bc} = \frac{bc}{ac}$
${bc}^{2} = ac \times cd \: \: \: \: \: \: \: \: equation \: (2)$
adding equation (1)&(2)
we get

${ab}^{2} = ad \times ac \:$
${bc}^{2} = ac \times \: cd$
ab^2+bc^2=ac×ad+ac×cd
ab^2+bc^2=ac(ad+cd)
ab^2+bc^2=ac×ac
ab^2+bc^2=ac^2
therefore
AC^2=AB^2+BC^2
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