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Segment addition postulate
AB + BC = AC

triangle sum theorem
all angles in a triangle add up to 180 degrees

vertical angle theorem
vertical angles are congruent.

angle addition postulate
if angle 3 is made of angles 1 and 2, angle 1 plus angle 2 = angle 3

linear pairs
if 2 angles are linear pairs, they are supplementary

alternate interior angle theorem
if two parallel lines are cut by a transversal, the pairs of alternat interior angles are congruent.

alternate exterior angles theorem
if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

sameside interior angles theorem
if two parallel lines are cut by a transversal, then the two pairs of sameside interior angles are supplementary.

common segments theorem
AB = CD, then AC = BD

converse corresponding angles postulate
if two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel

purpose of converse of angle theorems:
convert from equal angles to parallel lines

Perpendicular transversal theorem:
in a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

dual perpendicular theorem
if two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

Right angle congruence theorem
all right angles are congruent

congruent compliments theorem
if two angles are complementary to the same angle, the two angles are congruent.

congruent supplements theorem
if two angles are supplementary to the same angle, the two angles are congruent.

