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 congruent angles (or segments), they are congruent to each other. (Transitive Property)

THEOREM 17:

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

1. FG KJ2. GH KJ3. FG GH

4. KG bisects FH

1. Given2. Given3. 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 = 14We 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 33. 3 + 2 = 90°

1. Given2. Given3. Substitution (step 2

into step 1)