**Investigation of Centers of Triangles**

**By**

**Moni Olubuyide**

**The most common center of a triangle is the centroid. The centroid is like the center of gravity of a triangle. Let's explore **

CLICK HERE FOR ANIMATION OF CENTROID

**Notice that the distance from the median to the vertex is 2/3 of the length of the median. Secondly, the ratio of the distance from the vertex to the centroid compared to the centroid to the base of the median is 2:1. Another aspect of the centroid is that despite the type of triangle it will always be inside of the triangle....observe for yourself...**

**Now let's investigate another center of a triangle...the orthocenter. The orthocenter is the intersection of 3 lines containing the altitudes of the vertices of a triangle.**

**Notice that in an acute triangle the orthocenter lies inside of the triangle...**

**In a right triangle, the orthocenter is at a vertex of the triangle!! The side of a right triangle containing the right angle is also its altitude so it makes sense for the orthocenter to be at the vertex of this triangle....**

**In an obtuse triangle, the ortocenter is outside of the triangle!!! Unlike the centroid, the ortocenter moves freely depending on the type of triangle....**