Lesson 2 5 Addition and Subtraction Properties Objective

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.

A 3 cm 7 cm B 7 cm C D 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?

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

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

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

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

Theorem 13 If congruent segments (or angles) are subtracted from congruent segments (or angles), the differences are congruent. (Subtraction property) N Given: R Conclusion: O Statements Reasons 1. 2. 3. P

A Given: Conclusion: B ? E Statements Reasons 1. 2. F C D

Given: H G Conclusion: Statements Reasons E 1. 2. 3. 4. 5. 6. F

Summary… How are the addition and subtraction theorems that you just learned similar/different? Homework Lesson 2. 5 Worksheet