5.3 – Use Angle Bisectors of Triangles

Construct  line through point not on line A B Q

P 1.5cm D 4 cm 1.5cm Q  Bisector Thm

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

AD = 7

mDBA = 20°

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

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

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.

C A B **always inside the triangle

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

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

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

15

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

HW Problems #18 45° 45° 3x - 9 = 45 3x = 54 x = 18 B 5.3 313-314 WS 1, 3-7 odd, 10, 11-15 odd, 18, 19, 23 Constructing the Incenter and Angle Bisector Theorem #18 45° 45° 3x - 9 = 45 3x = 54 x = 18 B