1. Chapter 5 Perpendicular Bisectors

2. Perpendicular bisector A segment, ray or line that is perpendicular to a segment at its midpoint

3. Perpendicular bisector theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

4. A B C P Creates an isosceles triangle!

5. ExamplesNon-Examples

6. Concurrent lines When three or more lines (rays or segments) intersect in the same point Point of concurrency The point of the intersection of the lines

7. Circumcenter Point of concurrency of the perpendicular bisectors of the triangle.

8. Circumcenter: Is inside an acute triangle Circumcenter!

9. Is on a right triangle

10. Is outside an obtuse triangle

11. Acute - Inside Right - On Obtuse - Outside

12. Perpendicular bisector formula Circumcenter to vertices is equal distance.

13. P B C A

14. Why is this the case?? We can circumscribe the triangle by drawing a circle with the vertices of the triangle as points on the circle. The center of the circle is the circumcenter of the triangle for the perpendicular bisectors. The circumcenter to the vertices are the radii of the circle.