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

In ancient India,$\ldots \ldots \ldots$ altars were used for household rituals.

Write whether the following statement is True or False. Justify your answer.
If a quantity $B$ is a part of another quantity $A$,then $A$ can be written as the sum of $B$ and some third quantity $C$.

In the given figure,$C$ is the midpoint of $AB$ and $D$ is the midpoint of $AC$. Prove that $AD = \frac{1}{4} AB$. Mention the Euclid's axioms used in it.

State whether the following statement is true or false:
Only one line can pass through a single point.

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.