1. Bellwork  Given: is a perpendicular bisector to  Prove:

2. 4.4 Perpendicular Bisector Theorem Goal: Students will be able to apply the Perpendicular Bisector Theorem to proofs.

3. Perpendicular Bisector (Defn) The perpendicular bisector of a segment is the line that 1. Bisects the segment AND 2. Is perpendicular to the segment. Draw is the perpendicular bisector to

4. Perpendicular Bisector Theorem (Toolbox!)  If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of that segment.  We write:  Converse:  I say perpendicular bisector, you say _____________.

5. Let’s Prove the Converse:  If two points are each equidistant from the endpoints of a segment, then the two points determine the perpendicular bisector of that segment.  Given:  Prove:

6. Example 1  Given:  Prove:

7. Monday’s Problem #9 (in 5 steps!)  Given: Circle O  Prove:

8. Homework  Pg. 187 #2, 4, 6, 12, 14  Do these proofs WITHOUT using congruent triangles!  #2: 3 steps Ticket to Leave!  #4: 4 steps  #6: 3 steps  #12: 3 steps  #14: 4 steps Including the GIVEN!

9.  If perp bis, then bow.  If bow, then perp bis.