1. Date: Topic: Altitudes, Medians, and Bisectors ____ (6.4)
Warm-up: *Don’t forget to mark your diagram!!

2. Altitudes
An altitude of a triangle is a line segment through the ______ of an angle and is ________________ to the side opposite that angle.
Each triangle has ________ altitudes.
They intersect at a point called the _____________.
Sometimes the orthocenter is outside of the triangle

3. Constructing a perpendicular line from a point to a line (or segment)

4. Constructing Altitudes

5. Medians
The median of a triangle is a line segment joining a _________ of an angle to the ____________ of the side opposite that angle.
Each triangle has ________ medians.
They intersect at a point called the _________.

6. Constructing a midpoint

7. Constructing Medians

8. Bisectors
A perpendicular bisector is a _____ ________ passing through the midpoint of the segment and forming a ___ _______ angle.
The _______ perpendicular bisectors of a triangle intersect at a point, called the _____________.
An angle bisector is a line segment through the ________ of an angle, creating two angles of _______ _____________.
The _______ angle bisectors of a triangle intersect at a point, called the __________.

9. Constructing a perpendicular bisector

10. Constructing perpendicular bisectorsQ P

11. Constructing an angle bisectorQ

12. Constructing angle bisectorsP Q R

13. Mid-segments
A mid-segment is a line segment connecting the midpoints of ____ ________ of a triangle.
The mid-segment of a triangle is equal to ______ of the third side. ? 14
The mid-segment and the third side are ___________.
Example:
Find x:

14. Example:
is the perpendicular bisector of side
Find
and
3x + 5
4x - 6

15. Example:
is the angle bisector of
Find