2.3: Ángulo cero
- Page ID
- 114590
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\(\measuredangle AOA = 0\)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.
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.