This common perpendicular is called the base, the side opposite is the summit, and the angles adjacent to the summit are the summit angles. The asymptotic parallels through a point to a straight line make equal, acute angles with the perpendicular from the point to the straight line. If a straight line is the asymptotic parallel through a given point, in a given direction, to a given straight line, then it is, through each of its points, the asymptotic parallel in the given direction to the given straight line. If a straight line is asymptotically parallel, in a given direction, to a second straight line, then the second is asymptotically parallel in the same direction as the first. If two straight lines are asymptotically parallel, in the same direction, to the same straight line, then they are also asymptotically parallel, in that direction, to one another.
Asymptotic parallels approach each other in the direction of parallelism.
An exterior angle of a biangle is greater than the interior and opposite angle. If a straight line falling on two straight lines causes any one of the eight angle relationships to occur, then the two straight lines are divergently parallel. If an angle and the base of one biangle are equal, respectively, to an angle and the base of another biangle, then the other pair of angles is equal. If the two angles of one biangle are equal, respectively, to the two angles of another biangle, then the bases are equal. The base and summit of a Saccheri quadrilateral are divergently parallel, as are the other two sides.