Poincaré Disk - Hyperbolic Saccheri
ABCD is a Saccheri quadrilateral constructed in the Poincaré Disk model of hyperbolic geometry.
Point D is fixed to lie on a perpendicular to AB through A. Point C is fixed to lie on the intersection of a line perpendicular to AB through B and a circle of radius h with center B, where h is the distance from A to D, thereby ensuring the the length of segment AD equals the length of segment BC.
Points A, B, or D can be moved and point C will adjust accordingly, as will the angle measures shown on the left.
If either one of A or B is moved, it can be moved freely and the other will remain fixed in place. Point D can only be moved so that it remains on a line perpendicular to AB.
(Due to software limitations, sometimes C will "jump" to being on the opposite side of the AB that D is on. Unfortunately, I've not yet found a way to prevent this, but if it happens one can adjust A or B until C is on the correct side, or one can move D to be on the same side as C.)