**Geometry Chapter 5.3 Medians and Altitudes of a Triangle**

**I) Vocabulary:**

**A) Median of a triangle**- is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

**B) Centroid of the triangle**- the point of concurrency of the three medians of a triangle .

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

**D) Orthocenter of the triangle**- the point of concurrency of the three altitudes of a triangle.

**II) Theorems**:

**A) Concurrency of Medians of a Triangle**- the medians of a triangle intersect at a point that is called the centroid and that is two thirds of the distance from each vertex to the midpoint of the opposite side.

**Example**: If point P is the centroid of ΔABC, then AP = 2/3 AD, BP = 2/3 BF, and CP = 2/3 CE.

**B) Concurrency of Altitudes of a Triangle**- the lines containing the altitudes of a triangle are concurrent at the orthocenter.

**Example**: If AE, BF, and CD are the altitudes of ΔABC, then the lines AE, BF and CD intersect at the orthocenter point H.