Given a triangle with vertices $A$, $B$, and $C$, and point $D$ inside the triangle, which of the following must be true for point $D$ to be the orthocenter of the triangle?

• A. Point $D$ is the intersection of the three angle bisectors of triangle $ABC$.
• B. Point $D$ is the intersection of the perpendicular bisectors of the sides of triangle $ABC$.
• C. Point $D$ is the intersection of the three medians of triangle $ABC$.
• D. Point $D$ is the intersection of the three altitudes of triangle $ABC$.

Answer: (D)

Verified step by step guidance

1. Recall the definition of the orthocenter of a triangle: it is the point where the three altitudes of the triangle intersect. An altitude is a perpendicular segment from a vertex to the line containing the opposite side.
2. Understand the difference between various special points in a triangle: the incenter is the intersection of the angle bisectors, the circumcenter is the intersection of the perpendicular bisectors of the sides, and the centroid is the intersection of the medians.
3. Identify that the problem asks which condition must be true for point D to be the orthocenter, so we need to focus on the property involving altitudes.
4. Recognize that if point D is the intersection of the three altitudes of triangle ABC, then by definition, D is the orthocenter.
5. Therefore, the correct condition for D to be the orthocenter is that it is the intersection of the three altitudes of triangle ABC.