Parallel Lines

Front 1

Theorem 9-1

Back 1

Two parallel lines lie in exactly one plane

Front 2

Theorem 9-2

Back 2

In a plane, two lines are parallel if they are both perpendicular to the same line.

Front 3

The Parallel Postulate

Back 3

Through a given external point there is only one line parallel to a given line

Front 4

Theorem 3.1

Back 4

If two parallel planes are intersected by a 3rd plane, then the lines of intersection are parallel.

Front 5

PCA Postulate

Back 5

If parallel lines have a transversal then corresponding angles are congruent

Front 6

Theorem 3.2 PAI Theorem

Back 6

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

Front 7

Theorem 3.3 PAE Theorem

Back 7

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

Front 8

Theorem 3.4 PSSIA Theorem

Back 8

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

Front 9

Theorem 3.5

Back 9

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

Front 10

Postulate 13

Back 10

If two lines have a transversal and a pair of congruent corresponding angles, then the lines are parallel.

Front 11

Theorem 3.6

Back 11

If two lines have a transversal and a pair of congruent alternate interior angles, then the lines are parallel.

Front 12

Theorem 3.7

Back 12

If two lines have a transversal and a pair of congruent alternate exterior angles, then the lines are parallel.

Front 13

Theorem 3.8

Back 13

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

Front 14

Theorem 3.10

Back 14

If two lines are parallel to a third line, then they are parallel.