Bentley Triangle Orthocenter Construction and Properties

This GeoGebra example demonstrates the construction of the orthocenter of a triangle by drawing the three altitudes (perpendicular lines from each vertex to the opposite side) and finding their common intersection point. It visually shows how the orthocenter relates to the triangle's vertices and sides, and how its position changes with the triangle's shape. Core mathematical concepts include the definition of the orthocenter, properties of altitudes, and angle relationships (α, β, γ) involving the orthocenter. Construction steps use GeoGebra commands: Polygon to create the triangle, Line for sides, OrthogonalLine to draw altitudes from vertices, Intersect to find the orthocenter as the intersection of two altitudes, and Angle to label relevant angles. This resource is suitable for middle school (advanced) or high school students learning triangle centers, geometric construction, and exploring how the orthocenter lies inside, on, or outside the triangle for acute, right, or obtuse triangles respectively.