1. 5.3 – Use Angle Bisectors of Triangles

2. Construct  line through point not on line AB P Q

3. D 4 cm  Bisector Thm P Q 1.5cm

4. Angle Bisector Thm If a point is on the angle bisector, then it is congruent from the sides of the angle. Angle Bisector Converse If a point is equidistant from the sides of an angle, then it lies on the bisector of the angle

5. 1. given 3. given 5. Def. of  lines 6. Reflexive 7. AAS  ABC   ADC AC is the angle bisector of  BAD BC  AB, CD  AD AC is the angle bisector of  BAD BC  AB A B C D  ABC   ADC 4. given CD  AD  ABC   ADC 2. Def. of angle bisector  BAC   DAC

6. AD = 7

7. m  DBA = 20°

8. 6. Find x. 5x – 2 = 4x + 5 x – 2 = 5 x = 7

9. 6. Find x. 4x + 3 = 8x – 9 3 = 4x – 9 12 = 4x 3 = x

10. Construct a triangle with the given sides. Then construct the perpendicular bisector for each side of the triangle. What do you notice? A B AC B C

11. AB C

12. A B C

13. Special SegmentDefinition Angle Bisector Line that bisects the angle of a triangle

14. Concurrency PropertyDefinition Incenter Point equidistant from the sides of the triangle

15. 15

16. Point G is the incenter of  ACE. Find BG. 16