T RANSITIVE AND S UBSTITUTION P ROPERTY Lesson 2.7

Suppose  A   B and  A   C. Is  B   C?

T HEOREM 16: If angles (or segments) are congruent to congruent angles (or segments), they are congruent to each other. (Transitive Property) T HEOREM 17: If angles (or segments) are congruent to the same angle (or segment), they are congruent to each other. (Transitive Property)

1.FG  KJ 2.GH  KJ 3.FG  GH 4.KG bisects FH 1.Given 2.Given 3.If segments are  to the same segment, they are . (Transitive Property) 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 m  A = x + 10 to find m  A = = 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 (step 2 into step 1)