gen-briefly-explain-the-centroid-of-a-triangle-and-one-common-mi-7eee

Briefly explain the centroid of a triangle and one common misconception about it.

## The Centroid of a Triangle The **centroid** is the point where the three medians of a triangle intersect. A median is a line segment connecting a vertex to the midpoint of the opposite side. The centroid is located 2/3 of the distance from each vertex along its median and serves as the triangle's "center of mass" or balance point. ## Common Misconception Many people mistakenly believe the centroid is always at the **center** of the triangle in terms of being equidistant from all three vertices or sides. In reality, the centroid is only equidistant from the vertices in an **equilateral triangle**. In other triangles (scalene or isosceles), the centroid's position shifts toward the side with the longer base or toward wherever the "mass" of the triangle is concentrated. It's the balance point, not necessarily the geometric center.