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2.3: Ángulo cero

Última actualización

30 oct 2022
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- 2.2: Líneas y medias líneas
- 2.4: Ángulo recto

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Proposición $\PageIndex{1}$

$\measuredangle AOA = 0$ para cualquier $A \ne O$ .

Prueba

Según Axioma IIIb,

$\measuredangle AOA + \measuredangle AOA \equiv \measuredangle AOA$ .

Restar $\measuredangle AOA$ de ambos lados, eso lo conseguimos $\measuredangle AOA \equiv 0$ .

Por Axioma III, $-\pi < \measuredangle AOA \le \pi$ ; por lo tanto $\measuredangle AOA = 0$ .

Ejercicio $\PageIndex{1}$

Asumir $\measuredangle AOB = 0$ . $[OA) = [OB)$ Demuéstralo.

Pista: Por Proposición $\PageIndex{1}$ , $\measuredangle AOA = 0$ . Queda por aplicar Axioma III.

Teorema $\PageIndex{2}$

Para cualquiera $A$ y $B$ distinto de $O$ , tenemos

$\measuredangle AOB \equiv - \measuredangle BOA.$

Prueba

Según Axioma IIIb,

$\measuredangle AOB + \measuredangle BOA \equiv \measuredangle AOA$

Por Proposición $\PageIndex{1}$ , $\measuredangle AOA = 0$ . Hence the result.

Proposición2.3.1\PageIndex{1}

Teorema2.3.2\PageIndex{2}

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Proposición $\PageIndex{1}$

Teorema $\PageIndex{2}$