Plane geometry problem with parallel lines

Question

I know that i have two parallel lines ($d$ and $d'$) and a secant ($a$), the secant makes extern and intern angle that ar somehow congruent.

I'm thinking, is true that if i have two lines ($d$ and $d'$) (not knowing that are paralel) and a secant ($a$) as, $a \cap d =${$A$} and $a \cap d' =${$B$}, and I know that intern acute angles are congruent, this implies that $d$ and $d'$ are parallel?

Answer 1

You don't really know. In Euclidean geometry you assume it as an additional postulate. In other geometries, for instance (the most commonly used form of) spherical geometty, you can have the stated congruence with no parallel lines at all.