Practice 1-5: Basic Constructions of Angles and Quadrilaterals

This example provides a set of basic geometric construction exercises that demonstrate how to build common figures—such as angles and quadrilaterals (including trapezoids and rhombi/general quadrilaterals)—and how construction can encode metric relations tied to the geometric mean. The key mathematics includes angle construction and verification, fundamental properties of quadrilaterals (especially relationships involving parallelism/structure), trapezoid-defining side relations, and geometric mean (Geometric Mean) length proportions. Conceptually, the construction workflow is to decompose each target figure into standard ruler-and-compass steps: define key points, introduce auxiliary constructions (e.g., circles and perpendicular/angle-related constructions), and then use intersections to fix the required vertices. The original scrape provides no explicit GeoGebra command list, so the implementation should rely on standard construction objects—points, segments, lines, circles, and derived angle/parallel/perpendicular relations—forming a reproducible construction chain. Suitable for middle-school geometry instruction and for students preparing for higher-level geometry practice.