Orthocenter Construction in an Acute Triangle

This example demonstrates how the orthocenter of an acute triangle is obtained as the intersection point of the triangle’s three altitudes. It highlights the geometric phenomenon that for an acute triangle, all altitudes meet inside the triangle. The key concepts include orthocenter, altitudes (perpendicular lines from vertices to opposite sides), line intersection, and angle relationships using both explicit Angle objects and InteriorAngles to reflect internal angle structure. Construction approach: build triangle ABC with Polygon; generate the three altitude lines using OrthogonalLine (each through a vertex and perpendicular to the opposite side); compute the orthocenter as the intersection of two altitudes via Intersect (the construction also tracks the resulting point such as D); and use Angle together with InteriorAngles to display the relevant angle measures and confirm the right-angle/perpendicular conditions visually. The construction summary indicates objects like A, B, C, the intersection point D, and multiple angle variables (α, β, γ, δ, ε, ζ). Suitable for secondary school geometry instruction, interactive classroom demonstrations, and exploratory learning on triangle centers and geometric constructions.