1. Medians and Altitudes of a Triangle
Section 5-3
Medians and Altitudes of a Triangle

2. Median
A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

3. B C A

4. Centroid of the triangle
The point of concurrency of the three medians of a triangle.

5. B C A P

6. Concurrency of medians of a triangle theorem
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.

7. If P is the centroid of triangle ABC, then

8. altitude
The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side
Every triangle has three altitudes

9. B C A

10. Orthocenter of the triangle
The point where the altitudes of a triangle intersect.

11. B C A P

12. Concurrency of altitudes of a triangle Theorem
The lines containing the altitudes of a triangle are concurrent.