1. Triangle Bisectors 5.1 (Part 2)

2. SWBAT Construct perpendicular bisectors and angle bisectors of triangles Apply properties of perpendicular bisectors and angle bisectors of triangles

3. concurrent point of concurrency circumcenter circumscribed incenter inscribed Vocabulary

4. When three or more lines intersect at one point, the lines are said to be concurrent The point of concurrency is the point where the lines intersect

5. 5 Since a Triangle has three vertices... It has three Angle Bisectors. What did you notice about the Angle Bisectors of the Triangles? 5

6. Angle bisectors start at a vertex and bisect the angle. Incenter Angle Bisectors The Incenter is the Point of Concurrency of the Angle Bisectors

7. The incenter is always inside the triangle.

8. Any point on an angle bisector is equidistant from the sides of the angle

9. This makes the Incenter equidistant from all 3 sides

10. The incenter is the center of the triangle’s inscribed circle. A circle inscribed in a polygon intersects each line that contains a side of the polygon at exactly one point.

11. Since a Triangle has three sides... It has three Perpendicular Bisectors. What did you notice about the Perpendicular Bisectors of the Triangles?

12. A Perpendicular bisector of a side forms a 90° angle and bisects the side. a 90° angle and bisects the side. Circumcenter Perpendicular Bisectors The Circumcenter is the Point of Concurrency of the Perpendicular Bisectors

13. The circumcenter can be inside the triangle, outside the triangle, or on the triangle.

14. Recall: Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. A B C D AB is the perpendicular bisector of CD

15. This makes the Circumcenter equidistant from the 3 vertices

16. The circumcenter of Δ ABC is the center of its circumscribed circle. A circle that contains all the vertices of a polygon is circumscribed about the polygon.

17. Survival Training You’re Stranded On A Triangular Shaped Island. The Rescue Ship Can Only Dock On One Side Of The Island But You Don’t Know Which Side. At Which Point Of Concurrency Would You Set Up Camp So You Are An Equal Distance From All 3 Sides? INCENTER

18. What If The Ship Could Only Dock At One Of The Vertices? Would You Change The Location Of Your Camp ? If So, Where? YES CIRCUMCENTER CIRCUMCENTER