Altitudes and Orthocenters: Dynamic Geometry Exploration

①This GeoGebra example dynamically demonstrates that the three altitudes of a triangle intersect at a single point, the orthocenter, and extends the concept to general quadrilaterals. ②Core mathematical concepts include triangle altitudes, orthocenter, similarity transformations (dilation), and orthocentric properties of quadrilaterals, involving perpendicular lines and intersection points. ③Construction details: uses Line to draw sides, OrthogonalLine to construct altitudes, Point to mark vertices, Polygon to form the triangle, and Intersect to find the altitude intersection (orthocenter); objects include text labels text1-text4, points K/B/C/D/E, lines f/g/d/a/c/h/j, and polygon poly1, allowing dynamic dragging of vertices to observe orthocenter movement. ④Suitable for middle/high school geometry, math competitions, or introductory college geometry, helping students visualize the relationship between altitudes and orthocenters and explore generalizations to quadrilaterals.