1. Lesson 2.6 Multiplication and Division Properties Objective: After studying this lesson you will be able to apply the multiplication and division properties of segments and angles.

2. BEAF In the figure below, E, A, O, and F are trisection points. TU O A If BE = UO = 3, what can we say about If, is congruent to K M O N P R S J

3. Theorem 14 If segments (angles) are congruent, their like multiples are congruent (multiplication property of equality) Theorem 15 If segments (angles) are congruent, their like divisions are congruent (division property of equality)

4. Given: Prove: StatementsReasons 1. 2. 1. 3. ON AS E U 4.

5. Given: Conclusion: StatementsReasons 1. 2. 1. 3. 4. If angles are congruent, their like divisions (thirds) are congruent. (Division property) R T W X Y A C D E B

6. StatementsReasons 1. 2. 1. 3. Given: Prove: H J F G KM If segments are, their like multiples (doubles) are. (multiplication property)

7. StatementsReasons 1. 2. 1. Given: Prove: Y Z X U S A 3 1 3. 4. 3. 4. 5. 6. 5. 6. 7. Given Complements of Halves of. (An alternative form of the division property).

8. Lesson 2.6 Worksheet Homework Summary… How are the addition and subtraction theorems that you just learned similar/different?