1. Medians & Altitudes of Triangles
Median of a triangle -
Segments whose endpoints are a vertex of the triangle and the midpoint of the opposite side. A B C D
Median
Centroid of a triangle -
The point of concurrency (intersection) of the 3 medians of a triangle.
**the medians of a triangle intersect at a point that is 2/3 of the distance from each vertex to the midpoint of the opposite side. A B C D E F P
AP = AD
BP = BF
CP = CE

2. P is the centroid of QRS and PT = 5. Find RT and RP.
Example:
P is the centroid of QRS and PT = 5. Find RT and RP. R P S Q T
Example:
G is the centroid , BG = 27, find GF & BF. A B C D E F G

3. Altitude of a triangle -
Perpendicular segment from a vertex to the opposite side.
**can lie inside, outside, or on the triangle.
*orthocenter – intersection of the 3 altitudes of a triangle.
Where is the orthocenter located in the following triangles?
1) Acute triangle 2) Obtuse Triangle