1. Chapter 5Perpendicular Bisectors

2. Perpendicular bisector • A segment, rayor 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. C P A B Creates an isosceles triangle!

5. Examples Non-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 Circumcenter!

10. Is outside an obtuse triangle Circumcenter!

11. Acute - Inside Right - On Obtuse - Outside

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

13. B P A C

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.