In the figure,if $\angle 1 = \angle 3$,$\angle 2 = \angle 4$ and $\angle 3 = \angle 4$,write the relation between $\angle 1$ and $\angle 2$,using an Euclid's axiom.
(N/A) Given: $\angle 1 = \angle 3$,$\angle 2 = \angle 4$ and $\angle 3 = \angle 4$.
Euclid's first axiom states that 'things which are equal to the same thing are equal to one another'.
Since $\angle 1 = \angle 3$ and $\angle 3 = \angle 4$,we have $\angle 1 = \angle 4$.
Now,we have $\angle 1 = \angle 4$ and $\angle 2 = \angle 4$.
By applying Euclid's first axiom,since both $\angle 1$ and $\angle 2$ are equal to the same angle $\angle 4$,it follows that $\angle 1 = \angle 2$.
Euclid's first axiom states that 'things which are equal to the same thing are equal to one another'.
Since $\angle 1 = \angle 3$ and $\angle 3 = \angle 4$,we have $\angle 1 = \angle 4$.
Now,we have $\angle 1 = \angle 4$ and $\angle 2 = \angle 4$.
By applying Euclid's first axiom,since both $\angle 1$ and $\angle 2$ are equal to the same angle $\angle 4$,it follows that $\angle 1 = \angle 2$.
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