Through a point not on a given line there passes not more than one parallel to the line. Two lines that are parallel to the same line are parallel to each other. A line that meets one of two parallels also meets the other. If two parallels are cut by a transversal, the alternate interior angles are equal. There exists a triangle whose angle-sum is two right angles.
Parallel lines are equidistant from one another.
There exist two parallel lines whose distance apart never exceeds some finite value. Similar triangles exist which are not congruent. Through any three noncollinear points there passes a circle. Through any point within any angle a line can be drawn which meets both sides of the angle. There exists a quadrilateral whose angle-sum is four right angles.