Construct an Isosceles Triangle Given One Side (GeoGebra Steps + Activities)

This example demonstrates how to construct an isosceles triangle when one side is given (by length and/or position), showing both the reasoning and the final drawing workflow. It focuses on the geometric phenomenon that the apex of an isosceles triangle can be located as the intersection of two circles determined by equal-length constraints from the endpoints of the given side. Key math concepts include isosceles triangles, congruence via equal corresponding sides, circle–point relationships, and constructing triangles using precise geometric dependencies. The construction uses GeoGebra commands such as Point, PointIn, Segment, Circle, and Polygon: Circle is used to build the two constraint circles around the given side’s endpoints, PointIn places candidate vertices on those circles, Segment connects the vertices and endpoints, and Polygon forms the completed triangle. The activity structure (with and without GeoGebra) makes it suitable for secondary-school geometry lessons, hands-on geometric construction practice, and instructional use in dynamic geometry environments.