The things which are double of the same thing are

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

State whether the following statement is True or False. Justify your answer.
"For every line $l$ and for every point $P$ not lying on a given line $l$,there exists a unique line $m$ passing through $P$ and parallel to $l$." This is known as Playfair's axiom.

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.

Read the following axioms:
$(i)$ Things which are equal to the same thing are equal to one another.
$(ii)$ If equals are added to equals,the wholes are equal.
$(iii)$ Things which are double of the same thing are equal to one another.
Check whether the given system of axioms is consistent or inconsistent.

............ is credited with giving the first known proof.