Prove that $(\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2$, if and only if $\overrightarrow a,\: \overrightarrow b$ are perpendicular, given $\overrightarrow a ≠ 0, \overrightarrow b ≠ 0$.

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