Prove that an equilateral triangle can be constructed on any given line segment.

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

Hint: Use play fairs axiom, which is equivalent to Euclid's fifth postulate.

Attempts to prove Euclid's fifth postulate using the other postulate and axioms led to the discovery of several other geometries.

Things which are equal to the same things are _____ to one another. (Equal$/$Not equal)

If equals are added to equals, the wholes are _____. (equal/unequal)

If equals are subtracted from equals, the remainders are _____. (Equal/Unequal)

Things which coincide with one another are _____ to one another (equal/unequal).

According to Euclid's Axiom, the whole is greater than the _____. $\left(\mathrm{part} / \mathrm{full}\right)$