Testing Similar Solids with Dilation and Intersections

This example demonstrates how students can build their own 3D solids (e.g., cylinder/pyramid-like shapes) and then test whether two solids are similar. It focuses on the math of similarity transformations—especially dilation (scaling)—including the similarity ratio and consistent correspondence of features such as corresponding lengths (height/edges) and faces. Construction centers on using Dilate to generate a scaled version of the solids and Intersect to compute key intersection points/edges that define the visible boundaries and alignment of the shapes. GeoGebra primitives such as Point, Line, Segment, and Surface are used to create feature points, supporting lines/segments, and the faces/sides of the 3D objects. The activity is well-suited for middle to high school geometry lessons and for inquiry-based learning in solid geometry and transformations.