Medians and centroids

6 videos
You've explored perpendicular bisectors and angle bisectors, but you're craving to study lines that intersect the vertices of a a triangle AND bisect the opposite sides. Well, you're in luck because that (medians) is what we are going to study in this tutorial. We'll prove here that the medians intersect at a unique point (amazing!) called the centroid and divide the triangle into six mini triangles of equal area (even more amazing!). The centroid also always happens to divide all the medians in segments with lengths at a 1:2 ration (stupendous!).

Triangle medians and centroids

VIDEO 8:59 minutes
Seeing that the centroid is 2/3 of the way along every median

Triangle medians and centroids (2D proof)

VIDEO 15:15 minutes
Showing that the centroid is 2/3 of the way along a median

Medians divide into smaller triangles of equal area

VIDEO 7:46 minutes
Showing that the three medians of a triangle divide it into six smaller triangles of equal area. Brief discussion of the centroid as well

Exploring medial triangles

VIDEO 11:33 minutes
What a medial triangle is and its properties

Proving that the centroid is 2-3rds along the median

VIDEO 6:56 minutes
Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median)

Median centroid right triangle example

VIDEO 9:00 minutes
Example involving properties of medians