If two straight lines cut one another, they make the vertical angles equal to one another.

For let the straight lines $AB$, $CD$ cut one another at the point $E$;I say that the angle $AEC$ is equal to the angle $DEB$,and the angle $CEB$ to the angle $AED$.For, since the straight line $AE$ stands on the straight line $CD$, making the angles $CEA$, $AED$, the angles $CEA$, $AED$ are equal to two right angles. [Prop 1.13]Again, since the straight line $DE$ stands on the straight line $AB$, making the angles $AED$, $DEB$,the angles $AED$, $DEB$ are equal to two right angles. [Prop. 1.13]But the angles $CEA$, $AED$ were also proved equal to two right angles;therefore the angles $CEA$, $AED$ are equal to the angles $AED$, $DEB$. [Post. 4] and [C.N. 1]Let the angle $AED$ be subtracted from each;therefore the remaining angle $CEA$ is equal to the remaining angle $BED$. [C.N. 3]Similarly it can be proved that the angles $CEB$, $DEA$ are also equal.Therefore etc.Q.E.D.[Porism: From this it is manifest that, if two straight lines cut one another, they will make the angles at the point of section equal to four right angles]