<s>[INST] In a right triangle, can $a+b=c?$ I understand that due to the Pythagorean Theorem, $a^2+b^2=c^2$, given that $a$ and $b$ are legs of a right triangle and $c$ is the hypotenuse of the same right triangle. However, most of the time, $a+b\neq c$. What I have been wondering is, is there any set of values for $a$, $b$, and $c$ that make the statement $a+b=c$ true?
 [/INST] Substituting $c = a + b$ into $a^2+b^2=c^2$ gives us $a^2+b^2=(a+b)^2$. Multiplying that out gives us $a^2+b^2=a^2+2ab+b^2$ which means $2ab=0$
So to satisfy both $c = a + b$ and $a^2+b^2=c^2$ either $a=0$ or $b=0$. 
The question then becomes a bit more philosophical. We have a result that satisfies the Pythagorean equation but can we really consider it a right angle triangle? Is a "side" of length zero really a side at all?
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