Euclid divided his famous treatise "The Elements" into:

State whether the following statement is True or False and justify your answer:
Euclid's fourth axiom states that things which coincide with one another are equal to one another.

Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $AC = DC$ and $CB = CE$. Show that $AB = DE$.

Euclid's fifth postulate is:

If a straight line falling on two straight lines makes the interior angles on the same side of it,whose sum is $120^{\circ}$,then the two straight lines,if produced indefinitely,meet on the side on which the sum of angles is

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