H Rectangle Construction: Orthocenter and Rectangle Geometry

This example demonstrates how to construct a rectangle using the orthocenter of a triangle, revealing the geometric relationship between the orthocenter, perpendicular lines, and rectangle vertices. Core mathematical concepts include the orthocenter (intersection of the three altitudes of a triangle), orthogonal lines, rectangle properties, and comparisons of power and linear functions. Construction steps: using GeoGebra commands Segment, OrthogonalLine, Point, Line, Intersect, and Polygon, the points A, B, segments f, g, point C, perpendicular lines h, i, intersection point D, and rectangle poly1 are created, with auxiliary objects a, b, c, d defined. This example is suitable for middle and high school geometry classes, helping students intuitively understand the orthocenter's properties and how to construct special quadrilaterals using perpendicular lines, while also enabling cross-topic exploration with function graphs.