Set 10 of Nets: Rhombi and Triangle Decomposition

This example demonstrates Set 10 of “nets” by constructing a composite geometric structure via systematic rotation and polygonal joining. It highlights how a rhombus framework can be decomposed into isosceles and right triangles, revealing consistent relationships among edges and angles. The key math ideas include properties of rhombi, triangle congruence/angle constraints for isosceles and right triangles, fraction-like parameterization of proportions, and trigonometric reasoning underlying the rotation geometry. In GeoGebra, the construction is driven by commands Point, Polygon, and Rotate: points such as A, B, C and parameterized vertices (q1, l, w, h, q2–q6) are created, then their rotated counterparts (e.g., q4', q2', q5', q3', q6', t') are generated using Rotate. Polygon objects assemble the resulting faces, while interactive controls (button1, button2) and parameters (t, t') support stepwise exploration. Suitable for secondary to early university geometry lessons, enrichment activities, and contest-style geometric construction practice.