Altitudes of a Triangle

This GeoGebra applet demonstrates the geometric construction of the altitudes of a triangle. By drawing a triangle and the perpendicular lines from each vertex to the opposite side, it visually illustrates the intersection of the three altitudes, known as the orthocenter, along with related geometric properties. The applet is suitable for middle or high school plane geometry instruction and helps students understand the definition of a triangle altitude, how to construct it, and the positional characteristics of the orthocenter under different triangle configurations. Students can interact with the applet by dragging the vertices of the triangle to observe how the altitudes and the orthocenter move in real time. This dynamic exploration allows learners to discover important patterns: in an acute triangle, the orthocenter lies inside the triangle; in a right triangle, the orthocenter coincides with the right-angle vertex; and in an obtuse triangle, the orthocenter lies outside the triangle. These observations reinforce the connection between triangle classification and the location of key geometric centers. The construction process shown in the applet follows the standard geometric definition of an altitude: a line segment drawn from a vertex perpendicular to the line containing the opposite side. Each altitude is constructed using the perpendicular tool in GeoGebra, and the point where all three altitudes intersect is highlighted as the orthocenter. This visual and interactive approach helps students move beyond rote memorization and develop a deeper conceptual understanding of triangle geometry. By engaging with this applet, students build intuition for geometric reasoning and proof-writing, as they can empirically verify properties that are later formalized in Euclidean geometry. Teachers can use this resource as a classroom demonstration, an exploratory activity, or a self-study tool to support lessons on triangle centers, perpendicularity, and the interplay between algebraic and geometric reasoning in the coordinate plane.