Euclid was a native of $\ldots \ldots \ldots .$

Solve the following question using an appropriate Euclid's axiom:
In the figure:
$AB = BC$,$M$ is the mid-point of $AB$ and $N$ is the mid-point of $BC$. Show that $AM = NC$.

It is known that if $x+y=10$,then $x+y+z=10+z$. The Euclid's axiom that illustrates this statement is:

The three steps from solids to points are:

Write whether the following statement is True or False. Justify your answer.
$A$ pyramid is a solid figure,the base of which is a triangle,square,or some other polygon,and its side faces are equilateral triangles that converge to a point at the top.

Consider the following statement: "There exists a pair of straight lines that are everywhere equidistant from one another." Is this statement a direct consequence of Euclid's fifth postulate? Explain.