1. Lesson 2.5 Addition and Subtraction Properties Objective: After studying this lesson you will be able to apply the addition and subtraction properties of segments and angles.

2. A B CD 7cm 3cm In the diagram above AB = CD. Do you think that AC = BD? Suppose that BC were 5 cm. Would AC = BD? Does the length of BC have any effect on whether AC = BD?

3. Theorem 8 If a segment is added to two congruent segments, the sums are congruent. (addition property of equality) Given: Prove: P Q RS StatementsReasons 1. 2. 1. 3. 4. 3. 4. Given Def. of congruent segments Addition Property of Equality Substitution 5. Def. of congruent segments

4. Theorem 9 If an angle is added to two congruent angles, the sums are congruent. (Addition Property of Equality) Theorem 10 If congruent segments are added to congruent segments, the sums are congruent.(Addition Property of Equality) Do you think that is necessarily congruent to ? P S O KRM

5. Theorem 11 If congruent angles are added to congruent angles, the sums are congruent. (Addition Property of Equality) WX Y T Do you think that is necessarily congruent to ?

6. Theorem 12 If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction property) O K N P R If KO = KP and NO = RP Is KN = KR?

7. Given: Conclusion: StatementsReasons 1. 2. 1. 3. O N R P Theorem 13 If a segment (or angle) is subtracted from congruent segments (or angles), the differences are congruent. (Subtraction property)

8. StatementsReasons 1. 2. 1. A E B F D Given: Conclusion: ? C

9. StatementsReasons 1. 2. 1. 3. 4. 3. 4. 5. 6. 5. 6. Given: Conclusion: H G E F

10. Lesson 2.5 Worksheet Homework Summary… How are the addition and subtraction theorems that you just learned similar/different?