Exercise 11 Page 472

Let's rewrite the proof so that AB=2* MB. In the fifth statement, we substitute MB with AM. If we instead substitute AM with MB we will have an equation relating MB and AB.

Statement	Reason
1. M is the midpoint of AB	1. Given
2. AM≅ MB	2. Definition of midpoint
3. AM = MB	3. Definition of congruent segments
4. AM + MB=AB	4. Segment Addition Postulate
5. MB + MB=AB	5. Substitution Property of Equality
6. 2* MB=AB	6. Distributive Property
7. AB=2* MB	7. Symmetric Property of Equality

To show that MB= 12AB, we have to go one step further compared to the last proof. By using the Division Property of Equality we can eliminate the 2 from the left-hand side.

Statement	Reason
1. M is the midpoint of AB	1. Given
2. AM≅ MB	2. Definition of midpoint
3. AM = MB	3. Definition of congruent segments
4. AM + MB=AB	4. Segment Addition Postulate
5. MB + MB=AB	5. Substitution Property of Equality
6. 2MB=AB	6. Distributive Property
7. MB= 12AB	7. Division Property of Equality