Question

if an orthocenter lies inside of a triangle, then the triangle must be
isosceles.
obtuse.
right.
acute.

Explanation:

To determine the type of triangle when the orthocenter lies inside, we analyze each option:

• Isosceles: An isosceles triangle can be acute, right, or obtuse. The position of the orthocenter depends on the angles, not just the side lengths. So this is not correct.
• Obtuse: In an obtuse triangle, the orthocenter lies outside the triangle. So this is incorrect.
• Right: In a right triangle, the orthocenter is at the vertex of the right angle. So this is incorrect.
• Acute: In an acute triangle (where all angles are less than \(90^\circ\)), the orthocenter lies inside the triangle. This matches the given condition.

Answer:

D. acute.