Question

The diagram at the right shows the orthocenter of an acute triangle. Drag vertex C to form a right triangle and an obtuse triangle. Which statements are true about the orthocenter? Check all that apply.

It lies inside an acute triangle.
It lies inside a right triangle.
It lies on a right triangle.
It lies on an obtuse triangle.
It lies outside an obtuse triangle.

Answer 1

Checked:
- It lies inside an acute triangle. — True. (All three altitudes meet inside for acute triangles.)
- It lies inside a right triangle. — False. (The orthocenter is at the right‑angle vertex, not in the interior.)
- It lies on a right triangle. — True. (For a right triangle the orthocenter is exactly the right‑angle vertex, which lies on the triangle.)
- It lies on an obtuse triangle. — False. (The orthocenter is not on an obtuse triangle’s sides or vertices.)
- It lies outside an obtuse triangle. — True. (For obtuse triangles the altitudes meet at a point outside the triangle.)