Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the definition of an altitude in a triangle?

A segment connecting the midpoints of two sides
A line segment drawn from one vertex perpendicular to the opposite side
A segment that bisects a vertex
A segment connecting two angles of the triangle

The correct answer is: A line segment drawn from one vertex perpendicular to the opposite side

An altitude in a triangle is defined as a line segment drawn from one vertex of the triangle to the opposite side, forming a right angle (90 degrees) with that side. This definition emphasizes both the starting point of the altitude at a vertex and its endpoint on the opposite side, underscoring the perpendicular relationship crucial to this concept in geometry. This property of forming a right angle is vital for several geometric calculations, such as finding the area of a triangle, where the altitude serves as a key component when using the formula: Area = 1/2 × base × height. Understanding this definition helps students recognize how altitudes function in the triangle's geometry and their significance in various mathematical applications and theorems.