If a straight-line falling across two straight-lines makes the alternate angles equal to one another then the (two) straight-lines will be parallel to one another.For let the straight-line $EF$, falling across the two straight-lines $AB$ and $CD$, make the alternate angles $AEF$ and $EFD$ equal to one another. I say that $AB$ and $CD$ are parallel. <prf> Thus, $AB$ and $CD$ are parallel.Thus, if a straight-line falling across two straight-lines makes the alternate angles equal to one another then the (two) straight-lines will be parallel (to one another).