1. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Theorem 5.2: Perpendicular Bisector Theorem
In a plane, if a point is on the perpendicular bisector of a segment, then it is __________ from the endpoints of the segment. A B C P

2. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Theorem 5.3: Converse of the Perpendicular Bisector Theorem
In a plane, if a point is equidistant from the endpoints of a segment, then it is on the ____________ _________ of the segment. A B C P D

3. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Example 1
Use the Perpendicular Bisector Theorem
AC is the perpendicular bisector of BD. Find AD. A B C
7x – 6 4x D
Solution

4. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors J K L 13 N M
Example 2
Use perpendicular bisectors
In the diagram, KN is the perpendicular bisector of JL.
What segment lengths in the diagram are equal?
Is M on KN?
Solution
KN bisects JL, so ____ = ____.
Because K is on the perpendicular bisector of JL, ____ = ____ by the Theorem 5.2.
The diagram shows that ____ = ____ = 13.
Because MJ = ML, M is ____________ from J and L.
equidistant
So, by the __________________________________________, M is on the perpendicular bisector of JL, which is KN.
Converse of the Perpendicular Bisector Theorem

5. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Checkpoint. In the diagram, JK is the perpendicular bisector of GH. H G F K
x + 1 2x
4.1 J
What segment lengths are equal?
Find GH.

6. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Theorem 5.4: Concurrency of Perpendicular Bisector of a Triangle
The perpendicular bisector of a triangle intersects at a point that is equidistant from the vertices of the triangle. A B C D F E P
If PD, PE, and PF are perpendicular bisectors, then PA = _____ = _____.

7. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Example 3
Use the concurrency of perpendicular bisectors M N O 7 P Q R S 9 2
The perpendicular bisectors of MNO meet at point S. Find SN.
Solution
Using ______________, you know that point S is _____________ from the vertices of the triangle.
Theorem 5.4
equidistant
So, _____ = _____ = _____.
_____ = _____
Theorem 5.4.
_____ = _____
Substitute.

8. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Checkpoint. Complete the following exercise.
The perpendicular bisector of ABC meet at point G. Find GC. A C B 12 D E F G 6 15
By ______________,
Theorem 5.4
_____ = _____ = _____.

9. Use Perpendicular Bisectors
5.2
Use Perpendicular Bisectors
Pg. 284, 5.2 #1-10