Parallel Lines and Transversals: Postulates and Theorems

Vocabulary practice flashcards reviewing the postulates, theorems, and their converses related to parallel lines, transversals, and angle relationships.

Postulate 11

If parallel lines have a transversal, then corresponding angles are congruent.

Theorem 3.2

If parallel lines have a transversal, then alternate interior angles are congruent.

Theorem 3.3

If parallel lines have a transversal, then alternate exterior angles are congruent.

Theorem 3.4

If parallel lines have a transversal, then interior angles on the same side of the transversal are supplementary.

Theorem 3.5

If a transversal intersecting two parallel lines is perpendicular to one of the lines, it is also perpendicular to the other line.

Postulate 12

Through a point not on a line, there is exactly one line parallel to the given line.

Postulate 13

If two lines have a transversal and a pair of congruent corresponding angles, then the lines are parallel (converse of Postulate 11).

Theorem 3.6

If two lines have a transversal and a pair of congruent alternate interior angles, then the lines are parallel (converse of Theorem 3.2).

Theorem 3.7

If two lines have a transversal and a pair of congruent alternate exterior angles, then the lines are parallel (converse of Theorem 3.3).

Theorem 3.8

If two lines have interior angles on the same side of the transversal that are supplementary, then the lines are parallel (converse of Theorem 3.4).

Theorem 3.9

If two coplanar lines are perpendicular to the same line, then they are parallel.