Substitutes for Postulate 5 Flashcards
Through a point not on a given line…
Through a point not on a given line there passes not more than one parallel to the line.
Two lines that are parallel to…
Two lines that are parallel to the same line are parallel to each other.
A line that meets one…
A line that meets one of two parallels also meets the other.
If two parallels are cut by a…
If two parallels are cut by a transversal, the alternate interior angles are equal.
There exists a triangle…
There exists a triangle whose angle-sum is two right angles.
Parallel lines are…
Parallel lines are equidistant from one another.
There exist two parallel lines…
There exist two parallel lines whose distance apart never exceeds some finite value.
Similar triangles exist which…
Similar triangles exist which are not congruent.
Through any three non…
Through any three noncollinear points there passes a circle.
Through any point within…
Through any point within any angle a line can be drawn which meets both sides of the angle.
There exists a quadrilateral…
There exists a quadrilateral whose angle-sum is four right angles.
Any two parallel lines…
Any two parallel lines have a common perpendicular.
