Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the relationship between the angles of a triangle and its altitude?

1. The altitude divides the angles into equal halves

2. The altitude is drawn to the longest side

3. The altitude does not impact the triangle's angle measures

4. The altitude creates two right angles with the base

The correct answer is: The altitude creates two right angles with the base

The correct answer highlights that an altitude in a triangle is defined as a line segment from a vertex perpendicular to the line containing the opposite side. This geometric property ensures that the altitude forms two right angles with the base of the triangle. This right-angle relationship is significant because it helps establish the right triangle alongside the original triangle, which can be useful for various calculations, such as finding area or using trigonometric ratios. In a triangle, while the altitude indeed creates two right angles between itself and the base, it does not inherently divide the angles into equal halves nor is it always drawn to the longest side; its positioning is determined by the vertex from which it is drawn. Furthermore, the presence of the altitude does not change the angle measures in the triangle; it maintains the original angles while establishing new right angles. Understanding this relationship is fundamental in geometry, as it assists in solving problems related to triangle dimensions and properties.