1. 7.1(b) Notes: Angle Bisectors Lesson Objective: Identify and use angle bisectors in triangles. CCSS: G.CO.10, G.MG.3

2. Lesson 1: Angle Bisector Theorem Draw / B. Construct the angle bisector of / B. B

3. Lesson 1: Angle Bisector Theorem Plot point F on the angle bisector. B

4. Lesson 1: Angle Bisector Theorem Construct FD | BD and FE | BE. F ● B

5. Lesson 1: Angle Bisector Theorem Why is FD FE? D F ● B E

6. Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Lesson 1: Angle Bisector Theorem D F ● B E

7. Lesson 1: Angle Bisector Theorem D F ● B E

8. Converse Angle Bisector Theorem: If a point on the interior of an angle is equi- distant from the sides of the angle, then it is on the bisector of an angle. Lesson 2: Converse Angle Bisector Theorem D F ● B E

9. Lesson 2: Converse Angle Bisector Theorem D F ● B E

10. Lesson 3: Using the Angle Bisector Theorem a. b. c.

11. Lesson 4: Incenter Theorem a. Construct the angle bisector of each angle. A B C

12. Lesson 4: Incenter Theorem b. Label the point of concurrency P. Construct PD | AB, PE | BC, and PF | CA. A B C

13. Lesson 4: Incenter Theorem c.Anchor at P. Draw circle P with radius PD. What do you notice about the circle? A B C

14. Lesson 4: Incenter Theorem A B C

15. Lesson 4: Incenter Theorem If P is the incenter of ΔABC, then PD = PE = PF. A B C

16. Lesson 5: Using the Incenter Theorem If P is the incenter of ΔXYZ, find each measure. a.PK b.m/ LZP

17. 7.1(b): Do I Get It? Yes or No 1. Find m/ BAC if m/ DAC = 37° and BC = DC. 2. Find BC if DC = 3x + 5 and BC = 6x – 7. 3.Find JF. 4.Find m/ JAC.

18. 7.1(b): Do I Get It? Continued Find each measure. 2.WZ3. RT