1. EXAMPLE 3 Use properties of equality Prove this property of midpoints: If you know that M is the midpoint of AB,prove that AB is two times AM and AM is one half of AB. GIVEN: M is the midpoint of AB. PROVE: a. AB = 2 AM b. AM = AB 2 1

2. STATEMENT REASONS EXAMPLE 3 Use properties of equality 1. M is the midpoint of AB. 2. AM MB 3. AM = MB 4. AM + MB = AB 1. Given 2. Definition of midpoint 3. Definition of congruent segments 4. Segment Addition Postulate 5.AM + AM = AB5. Substitution Property of Equality

3. EXAMPLE 3 Use properties of equality 6.2AM = AB a.a. AM = AB 2 1 7. b.b. 6. Distributive Property 7. Division Property of Equality

4. GUIDED PRACTICE for Example 3 GIVEN: M is the midpoint of AB. PROVE: a. AB = 2 AM b. AM = AB 2 1 WHAT IF? Look back at Example 3. What would be different if you were proving that AB = 2 MB and that MB = AB instead? 1 2 4.

5. GUIDED PRACTICE for Example 3 STATEMENT REASONS 1. M is the midpoint of AB. 2. AM MB 3. AM = MB 4. AM + MB = AB 1. Given 2. Definition of midpoint 3. Definition of congruent segments 4. Segment Addition Postulate 5.MB + MB = AB5. Substitution Property of Equality

6. GUIDED PRACTICE for Example 3 6.2 MB = AB a.a. MB = AB 2 1 7. b.b. 6. Distributive Property 7. Division Property of Equality ANSWER In step 5,6, and 7, AM would be replaced by MB