1. 5.3 – Use Angle Bisectors of Triangles

2. Construct  line through point not on lineA B Q

3. P
1.5cm D
4 cm
1.5cm Q
 Bisector Thm

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. AD = 7

6. mDBA =
20°

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

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

9. In your group, each person draw a different sized triangle
In your group, each person draw a different sized triangle. One should be scalene obtuse, one scalene acute, scalene right, and one isosceles. Then construct the angle bisectors of the triangle.

10. C A B
**always inside the triangle

11. Equidistant from the sides
Point of concurrency
Property
incenter
Equidistant from the sides

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

14. Concurrency Property
Definition
Point equidistant from the sides of the triangle
Incenter

15. 15

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

17. HW Problems #18 45° 45° 3x - 9 = 45 3x = 54 x = 18 B 5.3 313-314 WS
1, 3-7 odd, 10, odd, 18, 19, 23
Constructing the Incenter and Angle Bisector Theorem
#18
45°
45°
3x - 9 = 45
3x = 54
x = 18 B