State whether the following statement is true or false:
Things which are double of the same thing are equal to one another.

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 $BX = BY$.

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.

John is of the same age as Mohan. Ram is also of the same age as Mohan. State the Euclid's axiom that illustrates the relative ages of John and Ram.

The three steps from solids to points are:

Given two distinct points,there is a ......... line that passes through them.