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.

The orthocenter is where the triangle’s three altitudes meet. In an acute triangle, the altitudes intersect inside the triangle. In a right triangle, the two legs are altitudes, so they meet at the right-angle vertex; therefore, the orthocenter lies on the triangle. In an obtuse triangle, the altitudes intersect outside it.

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