How many altitudes can be drawn in a triangle?

How many altitudes can be drawn in a triangle?

• A. One
• B. Two
• C. Three
• D. Four

Answer: (C)

In any triangle, an altitude is a perpendicular segment from a vertex to the line containing the opposite side. Regardless of the type of triangle—whether it's scalene, isosceles, or equilateral—there are always three vertices, which allows for exactly three distinct altitudes. Each altitude is associated with one of the triangle's vertices, dropping down to the line that forms the opposite side. Since each vertex corresponds uniquely to one altitude, this leads to the conclusion that a triangle can indeed have three altitudes. Consequently, understanding the concept of altitudes reinforces the properties of triangles and their geometrical characteristics, demonstrating the relationship between angles and sides within these shapes. Thus, the correct answer is that three altitudes can be drawn in a triangle.

In any triangle, an altitude is a perpendicular segment from a vertex to the line containing the opposite side. Regardless of the type of triangle—whether it's scalene, isosceles, or equilateral—there are always three vertices, which allows for exactly three distinct altitudes. Each altitude is associated with one of the triangle's vertices, dropping down to the line that forms the opposite side.

Since each vertex corresponds uniquely to one altitude, this leads to the conclusion that a triangle can indeed have three altitudes. Consequently, understanding the concept of altitudes reinforces the properties of triangles and their geometrical characteristics, demonstrating the relationship between angles and sides within these shapes. Thus, the correct answer is that three altitudes can be drawn in a triangle.