Euclid belongs to the country:

Solve the following question using the appropriate Euclid's axiom:
In the figure,we have $BX = \frac{1}{2} AB$,$BY = \frac{1}{2} BC$ and $AB = BC$.
Show that $BX = BY$.

State whether the following statement is True or False. Justify your answer.
The boundaries of the solids are curves.

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.

In the figure,if $AC = BD$,then prove that $AB = CD$.

Euclid stated that all right angles are equal to each other in the form of