Proving a fact about the Pythagorean Theorem – math.stackexchange.com

Proving a fact about the Pythagorean Theorem – math.stackexchange.com

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I am having some trouble in proving a conjecture it ocurred to me some time ago. If $$c^2 = a^2 + b^2$$ Then can the following be proven? $$c < a + b$$ Is this statement always true?

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