1. Warm Up– in your notebook

3. Medians and Altitudes of a Triangle
Advanced Geometry

4. MEDIAN
A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

5. Point of Concurrency of Medians
The point of concurrency of all the medians is called the centroid of the triangle.

6. Centroid’s Location
The centroid is always located inside the triangle!

7. Theorem 5.7: Concurrency of Medians of a Triangle
The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

8. Centroid
The centroid is also the balancing point or center of gravity for a triangular region. The center of gravity is the point at which the region is stable under the influence of gravity.

9. Altitude
An altitude of a triangle is the perpendicular segment from a vertex to the opposite side or the line that contains the opposite side. It can lie inside, on, or outside the triangle.

10. Point of Concurrency of Altitudes
The lines containing the altitudes are concurrent and intersect at a point called the orthocenter of the triangle.

11. Orthocenter’s Location
An orthocenter can lie inside, on, or outside the triangle.

12. Theorem 5.8: Concurrency of Altitudes of a Triangle
The lines containing the altitudes of a triangle are concurrent.