Compass-and-Ruler Construction of an Equilateral Triangle (+ Activities)

This example demonstrates how to construct an equilateral triangle using only a compass and straightedge, then extends learning with activities both with and without GeoGebra. It focuses on the construction logic behind the equilateral condition: drawing circles centered at given points with equal radii, using their intersection to locate the third vertex, and finally forming the triangle. Key concepts include geometric construction procedures, circle–circle intersection, congruence via equal segment lengths (equilateral as a special case), and verification through perimeter/side-length reasoning. In GeoGebra, the workflow is built from commands such as Point, Segment, Circle, Intersect, and Polygon, using objects like the base points and segment (e.g., A, B, segmAB) to generate the constructed vertices and triangle. Suitable for middle/high school geometry lessons, classroom instruction, and construction-problem practice.