State whether the following statement is True or False. Justify your answer.
Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Solve the following question using appropriate Euclid's axiom:
In the figure:
$BM = BN$,$M$ is the mid-point of $AB$ and $N$ is the mid-point of $BC$. Show that $AB = BC$.

In the Book of Elements $1$,how many definitions are given?

State whether the following statement is true or false:
Two distinct lines cannot have more than one point in common.

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.

State whether the following statement is True or False. Justify your answer.
Euclidean geometry is valid only for curved surfaces.