Proving Statements on Triangle Congruence

• Congruent Angles


  Two angles are congruent angles if they have equal measures.
• Congruent Segments


  Two line segments are congruent segments if they have equal measures.
• Angle Bisector


  A line or a line segment is an angle bisector if it divides an angle into two angles with equal measures.
• Segment Bisector


  A line or a line segment is a segment bisector if it divides another line segment into two segments with equal measures.
• Perpendicular Lines


  Two lines are perpendicular if the two lines form a right angle.
• Right Angle


  An angle is a right angle if its measure is exactly 90°
• Vertical Angles


  Two angles are vertical angles if it is formed from two intersecting lines.
• Midpoint


  A point is a midpoint if it divides a line segment into two segments with equal measures.
• Reflexive Property of Equality (RPE)


  AB = AB
• Reflexive Property of Congruence (RPC)


  AB̅̅̅̅ ≅ AB̅̅̅̅
• Symmetric Property of Equality (SPE)


  If AB = CD, then CD = AB.
• Symmetric Property of Congruence (SPC)


  If AB̅̅̅̅ ≅ CD̅̅̅̅, then CD̅̅̅̅ ≅ AB̅̅̅̅.
• Transitive Property of Equality (TPE)


  If AB = CD and CD = EF, then AB = EF.
• Transitive Property of Congruence (TPC)


  If AB̅̅̅̅ ≅ CD̅̅̅̅ and CD̅̅̅̅ ≅ EF̅̅̅̅, then AB̅̅̅̅ ≅ EF̅̅̅̅.
• Addition Property of Equality (APE)


  If AB = CD, then AB + EF = CD + EF.
• Multiplication Property of Equality (MPE)


  If AB = CD, then AB ∙ EF = CD ∙ EF.
• Law of Substitution


  If AB + CD = EF and CD = GH, then AB + GH = EF.
• Right Triangle Congruence


  If ∠ABC and ∠DEF are right angles, then ∠ABC ≅ ∠DEF.
• Vertical Angle Theorem


  Vertical angles are congruent.
• Note that we end a proof using a tombstone symbol ∎. This is used to formally signify the end of a proof.