$A$ solid has.........

Read the following two statements which are taken as axioms:
$(i)$ If two lines intersect each other,then the vertically opposite angles are not equal.
$(ii)$ If a ray stands on a line,then the sum of two adjacent angles so formed is equal to $180^{\circ}$.
Is this system of axioms consistent? Justify your answer.

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.

The word $\ldots \ldots \ldots$ is used for the line segment by Euclid.

Euclid belongs to the country:

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 $AC = BC$.