1. 4-7 Medians, Altitudes, and Perpendicular Bisectors

2. Median
of a triangle is a segment from a vertex to the midpoint of the opposite side.

4. Altitude
Segment from a vertex perpendicular to the line containing the opposite side. In an acute triangle all 3 altitudes are inside the triangle.
Altitudes can be outside the triangle

5. Altitudes in right triangles
Two of the altitudes are the actual legs of the triangle.

6. Altitudes in an obtuse triangle
In an obtuse triangle, 2 of the altitudes are outside the triangle.
Red lines are altitudes for this triangle. Notice that some of them are outside of the triangle, and one is on the inside.

7. Perpendicular Bisectors
A line or ray that is perpendicular to a segment at the segment’s midpoint.

8. Theorem
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

10. Theorem
If a point is equidistant from the endpoints of a segment, then the point lies on the ___________ __________ of the segment.

11. Theorem
If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
What kinds of lines do we use to measure distance?

12. A X Z P C B Y

13. Theorem
If a point is equidistant from the sides of an angle, then the point lies on the bisector of the angle.

14. Centers of a triangle

15. Homework
Pg CE Pg Pg Pg