Question

for which type of triangle is the orthocenter always a vertex of the triangle?

right

obtuse

isosceles

equilateral

Explanation:

The orthocenter is the point where the altitudes of a triangle intersect. In a right triangle, the two legs are altitudes themselves, and they intersect at the right - angled vertex. For an obtuse triangle, the orthocenter lies outside the triangle. In an isosceles triangle (non - right isosceles) and an equilateral triangle (which is a special case of isosceles), the orthocenter is inside the triangle (for acute isosceles/equilateral) or has a different position, not coinciding with a vertex as a general rule like in right triangles. So the type of triangle where the orthocenter is always a vertex is a right triangle.

Answer:

A. Right