Theorem Organizer
Ways to prove angles congruent
 Vertical angles are 
 If two lines are , they form , adjacent angles
 Compliments of the same angle, or congruent angles, are 
 Supplements of the same angle or congruent angles are 
 When parallel lines are cut by a transversal, corresponding angles are 
 When parallel lines are cut by a transversal, alternate interior angles are 
 If two angles of one triangle are congruent to two angles of another triangle,
then the third angles are congruent
 Definition of an angle bisector
 All angles in an equiangular polygon are congruent
 Transitive property
 Substitution property
 Reflexive property
Ways to prove angles complementary
 If the exterior side of two adjacent, acute angles are , then the angles are
complementary
 The acute angles of a right triangle are complementary
 Definition of complementary angles
 Angle addition axiom
Ways to prove angles supplementary
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When parallel lines are cut by a transversal, interiors on the same side of the
transversal are supplementary
Definition of supplementary angles
Angle addition axiom
Ways to prove lines perpendicular
 If two lines form , adjacent angles, then the lines are 
 If a transversal is perpendicular to one of two parallel lines, then it is
perpendicular to the other one also
 Definition of perpendicular lines
Ways to prove lines parallel
 If two lines are cut by a transversal, and corresponding angles are congruent,
then the lines are parallel
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If two lines are cut by a transversal, and alternate interior angles are congruent,
then the lines are parallel
If two lines are cut by a transversal, and the same side interior angles are
supplementary, then the lines are parallel
In a plane, two lines perpendicular to the same line are parallel
Two lines parallel to a third line are parallel to each other