1. Medians and Altitudes of Triangles
Section 5.3
Medians and Altitudes of Triangles

2. Definitions
Median – A median is a line from a vertex of a triangle to the midpoint of the opposite side of the triangle.
Altitude – An altitude is a line from a vertex of a triangle that is perpendicular to the line containing the opposite side.

3. Centroid
The medians of a triangle are concurrent at a point called the centroid.
The centroid is two-thirds the distance from the vertex to the midpoint of the opposite side.
Centroid Diagram

4. Orthocenter
The altitudes of a triangle are concurrent at a point called the orthocenter.
Some interesting facts about the orthocenter
The orthocenter, centroid, and circumcenter are collinear. The line is called the Euler line.
Theorem - Take a triangle with vertices at A, B and C, and let H be its orthocenter. The orthocenter for any of the triangles formed from three of these four points is the fourth point.

5. Example

6. Homework
Pg 282 #8-12, 17-23, 45