Rectangle—All: Geometric Construction with Angles

This example demonstrates how to construct rectangles in the plane using geometric constraints, with angles and right-angle relationships built into the construction. It focuses on key geometry ideas: adjacent sides of a rectangle are perpendicular, and the rectangle is determined by controlled directions, intersection points, and angle verification. The construction uses GeoGebra tools to: define sides with Segment; create perpendicular edges via OrthogonalLine; generate and place vertices using Point and Intersect; measure and confirm essential properties with Angle (e.g., checking for right-angle conditions); and finally build the rectangle using Polygon (such as poly1), along with labeled angle variables (α, β, γ, δ, etc.). Suitable for middle and high school geometry lessons, especially for demonstrating geometric construction workflows and verifying rectangle properties visually.