Reasons for Statements when Writing Proofs
Definitions of terms
Algebraic Properties
Addition, Subtractions, Multiplication, and Division Properties
Reflexive Property: Any segment or angle is equal to itself, which also means it is congruent to itself. (AB = AB,
<XYZ = <XYZ )
Symmetric Property: The order of a statement can be rearranged. (AB = CD, so CD = AB, and <ABC = <RST, so
<RST = <ABC
Transitive Property: If two segments or angles are equal and one is equal to a third, then the first and last are
also equal. (AB = CD, CD = XY, then AB = XY or <ABC = <XYZ, < XYZ = <MSN, then <ABC = <MSN) Also work with
congruent angles and segments
Substitution Property: If two quantities are equal, one can replace the other in the proof.
Postulates, Theorems, Converses, and Corallaries
Linear Pair Postulate: If two angles are a linear pair then they are supplementary.
Congruent Supplements Theorem: If two angles are supplementary to an angle, then the angles are congruent.
Vertical Angles Postulate: If two angles are vertical, then they are congruent.
Segment Addition Postulate: If a point B is between points A and C, then AB + BC = AC.
Angle Addition Postulate: If a point E is in the interior of <ABC, then <ABE + <EBC = <ABC
Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then corresponding angles are
congruent.
Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles
are congruent.
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then alternate exterior angles
are congruent.
Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then consecutive interior
angles are supplementary.
Corresponding Angles Converse: If corresponding angles created when two lines are cut by a transversal are
congruent, then the lines are parallel.
Alternate Interior Angles Converse: If alternate interior angles created when two lines are cut by a transversal
are congruent, then the lines are parallel.
Alternate Exterior Angles Converse: If alternate exterior angles created when two lines are cut by a transversal
are congruent, then the lines are parallel.
Consecutive Interior Angles Converse: If consecutive interior angles created when two lines are cut by a
transversal are supplementary, then the lines are parallel.