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.

Explanation:

1. For an acute triangle: The orthocenter (the intersection of altitudes) lies inside the triangle. So "It lies inside an acute triangle" is true.
2. For a right triangle: The orthocenter lies at the right - angled vertex (on the triangle). So "It lies on a right triangle" is true (and "It lies inside a right triangle" is false).
3. For an obtuse triangle: The orthocenter lies outside the triangle. So "It lies outside an obtuse triangle" is true (and "It lies on an obtuse triangle" is false).

Answer:

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