properties of segment congruence - congruent segments are transitive, reflexive and symmetric.

properties of angle congruence - congruent angles are reflexive, symmetric, and transitive.

right angles congruence theorem - all right angles are congruent.

congruent supplements theorem - if two angles are supplementary to the same angle then they are congruent.

congruent complements theorem - if two angles are complementary to the same angle then they are congruent.

vertical angles congruence theorem - vertical angles are congruent.

corresponding angles theorem - corresponding angles are congruent

alternate interior angles theorem - alternate interior angles are congruent.

alternate exterior - congruent

consecutive interior - supplementary

converse - to prove lines are parallel

transitive property of parallel lines - if two lines are parallel to the same line then they are parallel to each other.

linear pair perpendicular theorem - if two lines intersect to form a linear pair of congruent angles then the lines are perpendicular.

perpendicular transversal theorem - in a plane if a transversal if perpindicular to one line, then the line parallel to that line is also perpendicular to the transversal.

lines perpindicular to a transversal theorem - if two lines are perpindicular to the same transversal then they are parallel