For every ray, there is an angle with the given ray as a side congruent to any given angle. Every segment has exactly one midpoint. Postulate 9 Every angle, except a straight angle, has exactly one bisector. The sum of the measures of the angles with the same vertex on one side of a line and with no interior points in common is 180 degrees. The sum of the measures of all angles around a common vertex and with no interior points in common is 360 degrees.
All right angles are congruent.
Theorem 6 Two perpendicular lines form four congruent right angles. Postulate 12 For a given point and a line in a plane, there is exactly one line through the point that is perpendicular to the given line. If two lines form congruent adjacent angles, then the lines are perpendicular. Theorem 8 Supplements of congruent angles are congruent. Corollary Supplements of the same angle are congruent.