Euclid's Thirteenth Proposition in the Poincaré Disk

Euclid's Thirteenth Proposition in the Poincaré Disk - http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI13.html If a straight line stands on a straight line, then it makes either two right angles or angles whose sum equals two right angles. Let any straight line AB standing on the straight line CD make the angles CBA and ABD. I say that either the angles CBA and ABD are two right angles or their sum equals two right angles. Now, if the angle CBA equals the angle ABD, then they are two right angles. But, if not, draw BE from the point B at right angles to CD. Therefore the angles CBE and EBD are two right angles.