Construction 7: Geometric Construction of an Equilateral Triangle

This GeoGebra example demonstrates the classical geometric construction of an equilateral triangle. The core mathematical concepts include the definition of an equilateral triangle (three equal sides and three equal 60-degree angles) and the property of circles having equal radii. The construction process involves drawing two overlapping circles centered at two vertices with the side length as the radius; the intersection of these circles determines the third vertex. In GeoGebra, this is achieved using the Circle, Intersect, and Segment tools. This example is highly suitable for middle school and high school geometry curricula, as well as for introductory lessons on geometric constructions and mathematical proofs.