Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the centroid of a triangle?

1. Point where all three angles meet

2. Point where three medians intersect

3. Point where all sides are equal

4. Point of the highest altitude

The correct answer is: Point where three medians intersect

The centroid of a triangle is defined as the point where the three medians intersect. A median is a line segment drawn from each vertex of the triangle to the midpoint of the opposite side. The intersection point of these three medians is known as the centroid. This point has a unique property: it is the center of mass or balance point of the triangle, and it divides each median into two segments that are in a 2:1 ratio, with the longer segment being closer to the vertex. The other options are not correct definitions of the centroid. The point where all three angles meet describes the vertex of the triangle, while the idea of all sides being equal relates to an equilateral triangle, not the centroid itself. The highest altitude refers to one of the perpendicular segments from a vertex to the opposite side but does not define the centroid at all. Understanding these distinctions helps clarify the geometric concept being addressed.