1. Lesson 2.7 Transitive and Substitution Properties Objective: After studying this lesson you will be able to apply the transitive properties of segments and angles. You will also be able to apply the substitution property.

2. A U Theorem 16 If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (transitive property) S

3. Theorem 17 If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. (transitive property)

4. A B The Substitution Property

5. Given: Prove: StatementsReasons 1. 2. 1. 3. F G K H J 4. If segments are congruent to the same segment, they are congruent If a line divides a segment into two congruent segments, it bisects the segment.

6. Given: Prove: StatementsReasons 1. 2. 1. 3. 3 2 1

7. PQ R 2y + a = x + y + a 2y = x + y y = x

8. Lesson 2.7 Worksheet Homework Summary… Explain how the transitive property and the substitution property will work in proofs?