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

2. Median
Median of a triangle is a segment from a vertex to the midpoint of the opposite side.
Medians intersect at a point called the centroid.

3. Centroid
The distance from the cintroid to the midpoint of the side is half the distance from the centroid to the vertex.

4. Altitude
Altitude of a triangle is the perpendicular segment from a vertex to the line that contains the opposite side.
The altitudes of a triangle intersect at the Orthocenter.

5. Perpendicular Bisector
Perpendicular Bisector of a segment is a line (or ray or segment) that is perpendicular to the segment at its midpoint.
The perpendicular bisectors of a triangle intersect at the circumcenter

6. Angle Bisectors
The angle bisectors of a triangle intersect at the incenter of a triangle.

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

8. Theorems Cont.
If a point lies on the bisector of an angle, then the point is equidistant from the sides of the angle.
If a point is equidistant from the sides of an angle, then the point lies on the bisector of an angle.