2 Warm-Up Name the property of equality that justifies each statement. 1) If 3x = 15 and 5y = 15, then 3x = 5y Substitution Property of Equality2) If 4z = -12, then z = -3 Division Property of Equality3) If AB = CD, and CD = EF, then AB = EF Transitive Property of Equality4) If 45 = m<A, then m<A = 45Symmetric Property of Equality
3 VocabularyTheorem 2-1: Congruence of segments is reflexive, symmetric, and transitive.
4 Example 1) Justify each step in the proof. QRSGiven: Points P, Q, R, and S are collinear.Prove: PQ = PS – QSStatementsReasonsPoints P, Q, R, and S are CollinearGivenPS = PQ + QSSegment Addition PostulatePS – QS = PQSubtraction Property of EqualityPQ = PS - QSSymmetric Property of Equality
5 Example 2) Justify each step in the proof. BCDGiven: Line ABCDProve: AD = AB + BC + CDStatementsReasonsLine ABCDGivenAD = AB + BDSegment Addition PostulateBD = BC + CDSegment Addition PostulateAD = AB + BC + CDSubstitution Property of Equality
6 Example 3) Fill in the blank parts of the proof. CGiven: AC is congruent to DFAB is congruent to DEProve: BC is congruent to EFDEFStatementsReasonsAC is congruent to DF;AB is congruent to DEGivenAC = DF;AB = DEDefinition of congruent segmentsAC – AB = DF – DESubtraction Property of EqualityAC = AB + BC;DF = DE + EFSegment Addition PostulateAC – AB = BC;DF – DE = EFSubtraction Property of EqualityDF – DE = BCSubstitution Property of EqualityBC = EFSubstitution Property of EqualityBC is congruent to EFDefinition of congruent segments
7 Example 4) Fill in the blank parts of the proof. Given: AB is congruent to XYBC is congruent to YZProve: AC is congruent to XZXYZBCStatementsReasonsAB is congruent to XY;BC is congruent to YZGivenAB = XYBC = YZDefinition of congruent segmentsAB + BC = XY + YZAddition Property of EqualityAB + BC = ACXY + YZ = XZSegment Addition PostulateAC = XZSubstitution Property of EqualityAC is congruent to XZDefinition of congruent segments