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I understand this may be quite simple but could anyone do this? Proof by contradiction is the method I'm supposed to use.

a level student
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    What class are you taking? Which tools do you have at your disposal that you think might be helpful? –  Sep 03 '19 at 17:15
  • Ah, I'm not sure how to explain this but I do A level maths and only have a graphical calculator – a level student Sep 07 '19 at 15:06

2 Answers2

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Construct a right-angled triangle with sides $a$ and $b$. Call its hypotenuse $c'$. Because $a^2+b^2=c^2$ (as supposed) and $a^2+b^2=c'^2$ (Pythagoras' theorem), it follows that $c^2=c'^2$, i.e. $c=c'$. This means that the original triangle and the newly-constructed triangle both have sides $a$, $b$ and $c$. Thus, they are congruent, so the original triangle was right-angled too.

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Hint: Use that $$c^2=a^2+b^2-2ab\cos\gamma$$

Dr. Sonnhard Graubner
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