If two straight-lines cut one another then they make the vertically opposite angles equal to one another.For let the two straight-lines $AB$ and $CD$ cut one another at the point $E$. I say that  angle $AEC$ is equal to (angle) $DEB$, and (angle) $CEB$ to (angle) $AED$. <prf>  Thus, the remainder $CEA$ is equal to the remainder $BED$ [C.N.~3]. Similarly, it can be shown that $CEB$ and $DEA$ are also equal.Thus, if two straight-lines cut one another then they make the vertically opposite angles equal to one another.