If $ABD$ and $ACD$, then $ABC$ or $ACB$.
Answer: Since $ABD$, by Axiom 5 $A$, $B$, and $D$ are three different collinear points, and by $ACD$, $A$, $C$, and $D$ are three different collinear points. By Axiom 4, there is exactly one line that contains two different points, which means that $A$, $B$, $C$, and $D$ are four different collinear points. By Axiom 7, only one of the following holds, $ABDC$, $ABCD$, $ACBD$ or $CABD$. Given $ACD$, $ABDC$ does not hold because it implies $ADC$ which cannot hold by Axiom 6. Similarly $CABD$ is not true. Given $ABD$ and $ACD$, either $ABCD$ or $ACBD$ holds, therefore $ABC$ or $ACB$ holds.
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