1. LESSON 38 Perpendicular and Angle Bisectors of Triangles

2. Vocabulary An angle bisector of a triangle divides an angle into two congruent angles The incenter of a triangle i s the point of concurrency of angle bisectors

3. The perpendicular bisector of a triangle d ivides a side into two congruent segments and is perpendicular to the side The circumcenter of a triangle is the point of concurrency of perpendicular bisectors

4. Inscribed circle i s a circle that contains only one point from each side of the polygon (red circle) Circumscribed circle i s a circle that contains all vertices of a polygon (green circle)

5. Properties of Incenter and Circumcenter

6. Where is the circumcenter for a(n)… Right TriangleObtuse Triangle

7. Theorem 38-1: Triangle Angle Bisector Theorem

8. Find AD, units are in feet

9. Application: City Planning

12. Review 1.What is the intersection of medians? Centroid 2.What is the intersection of altitudes? Orthocenter 3.What is the intersection of angle bisectors? Incenter 4.What is the intersection of perpendicular bisectors? Circumcenter Perpendicular and angles bisectors of triangles will prepare you for: ◦L◦Lesson 39: Inequalities in a Triangle ◦L◦Lesson 46: Triangle Similarity: AA, SSS, SAS ◦L◦Lesson 51: Properties of Isosceles and Equilateral Triangles ◦L◦Lesson 55: Triangle Midsegment Theorem