1. Bisectors of a Triangle
Section 5-2
Bisectors of a Triangle

2. Perpendicular bisector of a triangle
A line, ray, or segment that is perpendicular to a side of the triangle at the midpoint of the side.

3. Perpendicular Bisector

4. Concurrent lines Point of concurrentcy
When three or mores lines (rays or segments) intersect in the same point
Point of concurrentcy
The point of the intersection of the lines

5. The three perpendicular bisectors of a triangle are concurrent!

6. The point of concurrency:
Is inside an acute triangle

7. Is on a right triangle

8. Is outside an obtuse triangle

9. Circumcenter of a triangle
The point of concurrency of the perpendicular bisectors of the triangle.

10. Concurrency of perpendicular bisectors of a triangle theorem
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle

11. P B C A

12. ANGLE BISECTOR OF A TRIANGLE
A bisector of an angle of a triangle

13. Incenter of the triangle
The point of concurrency of the angle bisectors
Always lies inside the triangle!

14. B C A P

15. Concurrency of angle bisectors of a triangle theorem
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.

16. B C A D F E P