Parallel and Perpendicular Lines

Vertical angles are two nonadjacent angles formed by two intersecting lines. Vertical angles are congruent

Corresponding angles are on the same side of the traversal and are both above or below the parallel lines. Corresponding angles are congruent

Adjacent angles are side by side and have a common vertex and a common side

Alternate interior (exterior) angles are on alternate sides of the traversal and are in the interior (exterior) of the parallel lines. They are congruent

Same side interior angles lie on the same side of the transversal and are between the parallel lines. They are congruent

If two coplanar lines are cut by a transversal so that a pair of corresponding angles is congruent, then the two lines are parallel

If two coplanar lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel

If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel

If two coplanar lines are cut by a transversal so that a pair of same side interior angles is supplementary, then the two lines are parallel

A bisector divides a figure into two equal parts.
If BD bisects ABC, then the angles ABD and DBC are equal in measure