If $A$,$B$ and $C$ are three points on a line,and $B$ lies between $A$ and $C$ (see figure),then prove that $AB + BC = AC$.

(N/A) In the figure given above,the line segment $AC$ coincides with the sum of the line segments $AB$ and $BC$.
According to Euclid's Axiom $(4)$,things which coincide with one another are equal to one another.
Since the segment $AB + BC$ coincides with the segment $AC$,it follows that:
$AB + BC = AC$
Note that in this proof,it is assumed that there is a unique line passing through two distinct points.