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Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $\angle ABC = \angle ACB$ and $\angle 3 = \angle 4$. Show that $\angle 1 = \angle 2$.

Which of the following needs a proof?

In the figure,if $OX = \frac{1}{2} XY$,$PX = \frac{1}{2} XZ$ and $OX = PX$,show that $XY = XZ$.

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 $AB = BC$.

Study the following statement: "Two intersecting lines cannot be perpendicular to the same line". Check whether it is an equivalent version to Euclid's fifth postulate.

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