Is it possible to prove the converse of the Pythagoras theorem with out a geometric proof?.That is f

xonycutieoxl1

xonycutieoxl1

Answered question

2022-06-16

Is it possible to prove the converse of the Pythagoras theorem with out a geometric proof?.That is from a 2 + b 2 = c 2 to Θ = 90

Answer & Explanation

victorollaa5

victorollaa5

Beginner2022-06-17Added 16 answers

Let A B C be some arbitrary triangle with sides a , b , c, (assume that A B = a , B C = b , A C = c) such that
(1) a 2 + b 2 = c 2
We can construct D E Fwhich is right angled and has sides a , b , d (assume D E = a , E F = b , D F = d) such that d is length of the hypotenuse, i.e D E F = 90 . By Pythagorean theorem we have
(2) a 2 + b 2 = d 2
Now we can put (1) in (2) and get c 2 = d 2 . c , d > 0, hence c = d
We can use SSS to claim that A B C D E F, so A B C = D E F = 90 , hence A B C is right angled. Q.E.D

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?