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

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.

Solve the following question using appropriate Euclid's axiom:
Two salesmen make equal sales during the month of August. In September,each salesman doubles his sale of the month of August. Compare their sales in September.

State whether the following statement is true or false:
Euclid was a well-known student of Thales.

Boundaries of solids are:

Solve the following question using an appropriate Euclid's axiom:
In the figure,$X$ and $Y$ are the mid-points of $AC$ and $BC$ respectively,and $AX = CY$. Show that $AC = BC$.