1. Chapter 2Section 5 Verifying Segment Relations

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 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

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

4. Example 1) Justify each step in the proof. P Q R S Given: Points P, Q, R, and S are collinear. Prove: PQ = PS – QS 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

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

6. Example 3) Fill in the blank parts of the proof. A B C Given: AC is congruent to DF AB is congruent to DE Prove: BC is congruent to EF D E F 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

7. Example 4) Fill in the blank parts of the proof. A Given: AB is congruent to XY BC is congruent to YZ Prove: AC is congruent to XZ X Y Z B C 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