Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is an orthocenter in a triangle?

1. It is the center of the triangle's circumscribed circle

2. It is the intersection point of the triangle's angles

3. It is the point where the three medians intersect

4. It is the concurrent point of the three altitudes

The correct answer is: It is the concurrent point of the three altitudes

The orthocenter of a triangle is defined as the point where all three altitudes of the triangle intersect. An altitude is a perpendicular line segment drawn from a vertex to the opposite side. Because altitudes are created from each vertex and intersect at one unique point, this intersection is what establishes the orthocenter. In relation to the other options, the circumcenter would be the point where the perpendicular bisectors of the sides intersect, not the altitudes. The centroid is the point where all three medians intersect, which are different from the altitudes. The statement about the intersection of the triangle's angles does not relate to the definition of the orthocenter, as it focuses on angle bisectors rather than altitude lines. Therefore, recognizing that the orthocenter specifically arises from the concurrency of altitudes confirms why this answer is accurate.