Prove the Converse of the Pythagorean Theorem. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

@ganeshie8

Question

Prove the Converse of the Pythagorean Theorem. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

@ganeshie8

ikram002p · Answer

would u like to use the cosin law to prove it ?
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anonymous · Answer

uhh idk i gues if its easieer

ikram002p · Answer

by the cosine law
in any triangle ,have  the biggest side C

$\large c^2=a^2+b^2-2ab \cos\theta$ 
s,t $\theta$ is the angle in the oposite side of C

ikram002p · Answer

so , the inverse of phythagorian 
if 
$\large c^2=a^2+b^2$
prove that  $\theta =90ْ $

anonymous · Answer

yea i dont really understand this but keep going

ikram002p · Answer

u have two equation
$\large c^2=a^2+b^2-2ab\cos\theta $
$\large c^2=a^2+b^2$
$\large a^2+b^2=a^2+b^2-2ab\cos\theta $
so
$\large  2ab\cos\theta = 0$
but
$\large 2 \neq 0 $
$\large a \neq 0 $
$\large b \neq 0 $

then 
$\large \cos\theta =0  $
$\large \theta =\cos^{-1} 0 = 90ْ $

ikram002p · Answer

got it nw ?

anonymous · Answer

honestly no ive never heard of any of that im kinda only in th 10th grade

ikram002p · Answer

O.O
butu should heard of the cosine law !
it mintioned in 10th grade i guess :O
ok tell me , in ur book what sub there are ?

anonymous · Answer

i dont have any books i have online classes but let me rephrase that i know that ^^ but idk the cos thats the confusing part

ikram002p · Answer

hmm should i give u another prove ?

anonymous · Answer

please

ikram002p · Answer

ok..

anonymous · Answer

thank you

ikram002p · Answer

let this be our triangle
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anonymous · Answer

ok

ikram002p · Answer

and we are given
$AC^2 =AB^2+BC^2$

ikram002p · Answer

and we wanna prove that < B is right angle ok ?

anonymous · Answer

ok im with you

ikram002p · Answer

lets draw D , such that <BAD =90
and AD=CB 
ok ?
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anonymous · Answer

yup

ikram002p · Answer

ur with me untill now ?
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ikram002p · Answer

ok , good !
then triangle DAB is a right triangle
and you can find DB by phythagors right ?
$BD^2=AD^2+AB^2$
ok ?

ikram002p · Answer

but AD=BC 
right ?
so
$BD^2=AB^2+BC^2$
got this ?

ikram002p · Answer

ur okey with it untill nw ?

anonymous · Answer

yes  indeed i am

ikram002p · Answer

ok ok let me know if there is somthing u dint got in each step :D
let us continue

ikram002p · Answer

so from both equation 
$BD^2=AB^2+BC^2$
$AC^2=AB^2+BC^2$
its ovs that BD=AC right ?

anonymous · Answer

what is ovs?

ikram002p · Answer

ovs=obvious
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