$A$ statement that needs a proof is called a........

Consider the following statement: "There exists a pair of straight lines that are everywhere equidistant from one another." Is this statement a direct consequence of Euclid's fifth postulate? Explain.

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

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 $\angle 1 = \angle 2$.

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 Ancient India,altars with combinations of shapes like rectangles,triangles,and trapeziums were used for: