Euclid divided his famous treatise "The Elements" into:

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 $\angle 1 = \angle 2$.

The side faces of a pyramid are:

Solve the following question using an appropriate Euclid's axiom:
In the figure,$X$ and $Y$ are the mid-points of $AC$ and $BC$ respectively,and $AX = CY$. Show that $AC = BC$.

Solve the following question using appropriate Euclid's axiom:
Two salesmen make equal sales during the month of August. In September,each salesman doubles his sale of the month of August. Compare their sales in September.

Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $AB = BC$ and $BX = BY$. Show that $AX = CY$.