Pasch's Theorem

Theorem
Let $a, b, c, d$ be points on a line.

Let $\tuple {a, b, c}$ denote that $b$ lies between $a$ and $c$.

Then $\tuple {a, b, c}$ and $\tuple {b, c, d}$ together imply that $\tuple {a, b, d}$.

That is, if:
 * $b$ is between $a$ and $c$

and:
 * $c$ is between $b$ and $d$

then:
 * $b$ is between $a$ and $d$.

Also see

 * Outer Transitivity of Betweenness