1. Altitude, perpendicular bisector, both, or neither?
Warm-up E A
1. If CD = 3.25, what is BC? B
6.5 G
2. Find AG if DG = 10. D 20 C
3. If CG = 7, find CE?
10.5
Altitude, perpendicular bisector, both, or neither?
PER. BISECTOR
NEITHER
BOTH
ALTITUDE

2. Perpendicular Bisector
5-2
Perpendicular Bisector
perpendicular to a side at its midpoint

3. Perpendicular Bisector Theorem
5-2
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment

4. How many perpendicular bisectors does a triangle have?
The intersection of the perpendicular bisector is called the CIRCUMCENTER.
How many perpendicular bisectors does a triangle have?

5. What is special about the CIRCUMCENTER?
Equidistant to the vertices of the triangle.

6. Example 1: Point G is the circumcenter of the triangle. Find GB. 7 A 75 2 B C F 7

7. Example 2: Point G is the circumcenter of the triangle. Find CG. 10 A6 B 8 C F 10

8. cuts the angle into 2 equal parts
5-3
Angle Bisector
Angle Bisector
cuts the angle into 2 equal parts

9. The intersection of the angle bisectors is called the INCENTER.
How many angle bisectors does a triangle have?

10. What is special about the INCENTER?
Equidistant to sides of the triangle

11. Example 1: Point N is the incenter of the triangle.
Find the length of segment ON. 30 18 18

12. Example 2: Point N is the incenter of the triangle.
Find the length of segment NP. 15