Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the median of a triangle?

A segment from a vertex to the midpoint of the opposite side
A segment that is perpendicular to a side
A segment connecting two angles
A segment joining the midpoints of two sides

The correct answer is: A segment from a vertex to the midpoint of the opposite side

The median of a triangle is defined as a line segment that connects a vertex of the triangle to the midpoint of the opposite side. This means that the median divides the triangle into two smaller triangles of equal area. Since each triangle shares the base (the segment being the side of the triangle) and has a height determined by the vertex, this property confirms the effectiveness of the median in ensuring balance in area. In this context, understanding the role of the median is essential because it helps in various applications in geometry including areas and centroids of triangles. The other options present different segments that have specific definitions, but they do not align with the geometric definition of a median. The option that describes a median accurately reflects its characteristics within a triangle.