# 2.7 Transitive and Substitution Property

TRANSITIVE AND SUBSTITUTION PROPERTY Lesson 2.7 Suppose A B and A C. Is B C? THEOREM 16:

If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (Transitive Property) THEOREM 17: If angles (or segments) are

congruent to congruent angles (or segments), they are congruent to each other. (Transitive Property) 1. FG KJ 2. GH KJ 3. FG GH 1. Given 2. Given

3. If segments are to the same segment, they are . (Transitive Property)Transitive Property) 4. KG bisects FH 4. If a line divides a segment into two segments, it bisects the segments.

If A B, find m A. 2x 4 = x + 10 x = 14 We can now substitute 14 in for x in mA = x + 10 to find mA = 14 + 10 = 24. This is the Substitution Property. It can be applied when you have variables or not.

1. 1 + 2 = 90 2. 1 3 3. 3 + 2 = 90 1. Given 2. Given 3. Substitution (Transitive Property)step 2 into step 1)

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