Proposition 1: Construct an Equilateral Triangle on a Given Segment

① This example demonstrates how to construct an equilateral triangle on a given finite straight line segment. ② Core mathematical concepts include Euclidean geometric construction, the definition and properties of an equilateral triangle, and determining vertices via circle‑segment intersections. ③ Construction steps: use the Segment command to create the given segment AB; then draw circles centered at A and B with radius AB (implicit Circle command); their intersection provides the third vertex C; finally connect the three points with Polygon or Segment commands to form the equilateral triangle. ④ Suitable for middle‑school geometry lessons, high‑school geometry review, introductory geometric construction demos, and dynamic geometry software training.