 # Verifying Segment Relations

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Verifying Segment Relations
Chapter 2 Section 5 Verifying Segment Relations

Warm-Up Name the property of equality that justifies each statement.
1) If 3x = 15 and 5y = 15, then 3x = 5y  Substitution Property of Equality 2) If 4z = -12, then z = -3  Division Property of Equality 3) If AB = CD, and CD = EF, then AB = EF  Transitive Property of Equality 4) If 45 = m<A, then m<A = 45 Symmetric Property of Equality

Vocabulary Theorem 2-1: Congruence of segments is reflexive, symmetric, and transitive.

Example 1) Justify each step in the proof.
Q R S Given: Points P, Q, R, and S are collinear. Prove: PQ = PS – QS Statements Reasons Points P, Q, R, and S are Collinear Given PS = PQ + QS Segment Addition Postulate PS – QS = PQ Subtraction Property of Equality PQ = PS - QS Symmetric Property of Equality

Example 2) Justify each step in the proof.
B C D Given: Line ABCD Prove: AD = AB + BC + CD Statements Reasons Line ABCD Given AD = AB + BD Segment Addition Postulate BD = BC + CD Segment Addition Postulate AD = AB + BC + CD Substitution Property of Equality

Example 3) Fill in the blank parts of the proof.
C Given: AC is congruent to DF AB is congruent to DE Prove: BC is congruent to EF D E F Statements Reasons AC is congruent to DF; AB is congruent to DE Given AC = DF; AB = DE Definition of congruent segments AC – AB = DF – DE Subtraction Property of Equality AC = AB + BC; DF = DE + EF Segment Addition Postulate AC – AB = BC; DF – DE = EF Subtraction Property of Equality DF – DE = BC Substitution Property of Equality BC = EF Substitution Property of Equality BC is congruent to EF Definition of congruent segments

Example 4) Fill in the blank parts of the proof.
Given: AB is congruent to XY BC is congruent to YZ Prove: AC is congruent to XZ X Y Z B C Statements Reasons AB is congruent to XY; BC is congruent to YZ Given AB = XY BC = YZ Definition of congruent segments AB + BC = XY + YZ Addition Property of Equality AB + BC = AC XY + YZ = XZ Segment Addition Postulate AC = XZ Substitution Property of Equality AC is congruent to XZ Definition of congruent segments