Bellwork

1. Bellwork For the following problems, use A(5,10), B(2,10), C(3,3) Find AB Find the midpoint of CA Find the midpoint of AB Find the slope of AB

2. Bellwork Solution For the following problems, use A(5,10), B(2,10), C(3,3) Find AB

3. Bellwork Solution For the following problems, use A(5,10), B(2,10), C(3,3) Find the midpoint of CA

4. Bellwork Solution For the following problems, use A(5,10), B(2,10), C(3,3) Find the midpoint of AB

5. Bellwork Solution For the following problems, use A(5,10), B(2,10), C(3,3) Find the slope of AB

6. Use Angle Bisectors of Triangles Section 5.3

7. The Concept • Today we’re going to take a look at some special properties of Angle Bisectors

8. Theorem 5.5: Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Theorems Theorem 5.6: Converse of the Angle Bisector Theorem If a point is in the interior of an angle and is equidistant from the sides of an angle, then it lies on the bisector of the angle C D A B

9. Find x Example C x 27o D A 27o 15 B

10. C Example Find x & y 5y-8 35o D A 4x-1o 3y+12 B

11. Theorem 5.7: Concurrency of Angle Bisectors of a Triangle The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle Theorem This point of concurrency is called the incenter. Circles centered at this point will equally touch all three sides of the triangle

12. Homework 5.3 Exercises 3-20, 24, 25, 34, 35

13. Angle Bisector Theorem • Incenters Most Important Points