Constructing and Exploring Pyramids in 3D Geometry

① This example demonstrates how to construct a pyramid using GeoGebra's 3D tools, showing the vertices, base, lateral faces, and auxiliary lines such as altitudes and midpoints. ② Core mathematical concepts include solid geometry: pyramid definition, lateral triangular faces, base polygon, perpendicular from apex to base (height), and special points like midpoints and orthocenters; it also touches on complex numbers, natural numbers, isosceles triangles, and orthocenters, but focuses on 3D pyramid construction. ③ Construction highlights: from the summary, commands include Polygon (to create the base), Pyramid (to generate the solid), Midpoint (to find midpoints), OrthogonalLine (to draw perpendiculars), Intersect (to find intersections), Segment (to connect edges), and Angle (to measure angles); objects include vertices A, B, C, D, base poly1, lateral faces faceABD, faceBCD, faceACD, and edges edgeAD, edgeBD, edgeCD, illustrating a complete workflow from 2D polygon to 3D solid. ④ Suitable for high school or early college solid geometry teaching, or math lab sessions, helping students intuitively understand pyramid structure, relationships between lateral faces and base, and positions of special points like orthocenters. By dynamically adjusting vertex positions, learners can observe shape changes and deepen spatial reasoning.