1. Verifying Segment Relations
Chapter 2 Section 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.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

5. 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

6. 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

7. 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