Constructing Equilateral Triangles: Classic Compass-and-Straightedge

① This example demonstrates how to construct an equilateral triangle using compass and straightedge techniques, implemented in GeoGebra with circles, segments, and intersection points, while dynamically displaying the side lengths. ② The core mathematical concepts include the definition of an equilateral triangle (all sides equal, all angles 60°) and the fundamental principle of geometric construction: drawing two circles with a common radius and using their intersection as the third vertex. ③ Construction details: from the summary, the Circle command creates two congruent circles centered at A and B, Segment connects the intersection point C to A and B, Intersect finds the circle intersections, Distance measures the three side lengths, Midpoint may be used for auxiliary purposes, and Text objects display the measured lengths. ④ Suitable for middle school geometry classes to explore triangle properties, construction logic, and the use of measurement and text annotations in dynamic geometry software.