Construction and Properties of the Orthocenter of a Triangle

This applet demonstrates the geometric construction and properties of the orthocenter of a triangle. Given the three vertices of a triangle, the applet constructs the altitudes from each vertex to the opposite side using orthogonal lines. An altitude is defined as a line segment drawn from a vertex perpendicular to the opposite side, also called the base. Once all three altitudes are drawn, their point of intersection is identified as the orthocenter. The applet allows users to drag the vertices of the triangle, observing in real time how the altitudes adjust and how the orthocenter moves accordingly. This dynamic interaction helps students understand how the position of the orthocenter varies depending on the type of triangle: for an acute triangle, the orthocenter lies inside the triangle; for a right triangle, the orthocenter coincides with the vertex at the right angle; and for an obtuse triangle, the orthocenter lies outside the triangle. The applet is designed for students studying plane geometry, particularly the special points of triangles. It reinforces key definitions, including altitude, orthocenter, perpendicularity, and concurrency. By interacting with the construction, learners can explore the relationship between the shape of a triangle and the location of its orthocenter, deepening their conceptual understanding beyond rote memorization. The applet is well suited for classroom demonstrations, independent exploration, and formative assessment activities in high school geometry courses.