1. PROVE STATEMENTS ABOUT SEGMENTS & ANGLES

2. EXAMPLE 1 Write a two-column proof Write a two-column proof for the situation in Example 4 on page 107. GIVEN: m  1 = m  3 PROVE: m  EBA = m  DBC 1. m  1 = m  3 2. m  EBA = m  3 + m  2 3. m  EBA = m  1 + m  2 1. Given 2. Angle Addition Postulate 3. Substitution Property of Equality STATEMENT REASONS

3. EXAMPLE 1 Write a two-column proof 5. m  EBA = m  DBC 4. m  1 + m  2 = m  DBC 4. Angle Addition Postulate 5. Transitive Property of Equality

4. GUIDED PRACTICE for Example 1 GIVEN : AC = AB + AB PROVE : AB = BC 1. Four steps of a proof are shown. Give the reasons for the last two steps. 1. AC = AB + AB 2. AB + BC = AC 3. AB + AB = AB + BC 4. AB = BC 1. Given 2. Segment Addition Postulate STATEMENT REASONS 3. ? 4. ?

5. GUIDED PRACTICE for Example 1 GIVEN : AC = AB + AB PROVE : AB = BC ANSWER 1. AC = AB + AB 2. AB + BC = AC 3. AB + AB = AB + BC 4. AB = BC 1. Given 2. Segment Addition Postulate 3. Transitive Property of Equality 4. Subtraction Property of Equality STATEMENT REASONS

6. EXAMPLE 2 Name the property shown Name the property illustrated by the statement. a.a. If R T and T P, then R P. b.b. If NK BD, then BD NK. SOLUTION Transitive Property of Angle Congruence a.a. b.b. Symmetric Property of Segment Congruence

7. GUIDED PRACTICE for Example 2 2. CD CD 3. If Q V, then V Q. Reflexive Property of Congruence ANSWER Symmetric Property of Congruence ANSWER

8. EXAMPLE 4 Solve a multi-step problem GIVEN: B is the midpoint of AC. C is the midpoint of BD. PROVE: AB = CD STATEMENT REASONS 1. B is the midpoint of AC. C is the midpoint of BD. 1. Given 2. Definition of midpoint 2. AB BC 3. BC CD 3. Definition of midpoint

9. EXAMPLE 4 Solve a multi-step problem 5.AB = CD 4. AB CD 4. Transitive Property of Congruence 5. Definition of congruent segments