Solve the equation $a-15=25$ and state which axiom do you use here.

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.

The total number of propositions in the Elements are:

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 $BX = BY$.

Ram and Ravi have the same weight. If they each gain weight by $2\, kg$,how will their new weights be compared?

Write whether the following statement is True or False. Justify your answer.
"The statements that are proved are called axioms."