PROOF
Let the straight lines AB, CD intersect one another at the point E;
then angle AEC is equal to angle DEB, and angle CEB is equal to angle AED.
For, since the straight line AE stands on the straight line CD, making
angles AED, AEC, then those angles are equal to two right angles.
And since the straight line DE stands on the straight line AB, making angles
AED, DEB, then those angles also are equal to two right angles.

Therefore, angles AED, AEC are equal to angles AED, DEB.
From each pair, subtract angle AED.

Therefore the remaining angle AEC is equal to the remaining angle DEB.

Therefore, when two straight lines etc.

Q.E.D.