Properties of Parallel Lines:

Postulate:

If two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

Theorem:

If two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

Theorem:

If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary.

Theorem:

If the transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other one as well.

Postulate:

If two lines are intersected by a transversal and their corresponding angles are congruent then, the lines are parallel.

Theorem:
If two lines are intersected by a transversal and their alternate interior angles are congruent then, the lines are parallel.

Theorem:

If two lines are intersected by a transversal and the same-side interior angles are supplementary then, the lines are parallel.

Theorem:

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

Theorem:

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

Theorem:

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

Theorem:

If two lines are parallel to a third line then they are all parallell to each other.

Theorem:

If three parallel lines cut congruent segments off a transversal then, they cut off congruent segments on every transversal.

Corollary:

A line that contains the midpoint of one of the sides of a triangle and is parallel to another side bisects the third side of the triangle.