PRINCIPIA · THEOREM

Complements of the same angle are equal

Dependencies: Protractor axiom (angles can be treated as real numbers).

Statement

Let $\alpha$ and $\beta$ both be complementary to the same angle $\gamma$ :

\alpha + \gamma = 90^{\circ},\qquad \beta + \gamma = 90^{\circ}.

Then $\alpha = \beta$ .

$Two right angles are split into \alpha + \gamma and \beta + \gamma, sharing the same \gamma ⇒ \alpha = \beta$

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