Triangle Construction: Given Side, Height & Median

This GeoGebra example demonstrates the geometric construction of a triangle when given the length of one side, the altitude (height) to that side, and the median to the same side. It explores the necessary conditions for a unique triangle and uses circle intersections and segment tools to locate the third vertex. Core mathematical concepts include triangle inequalities, properties of medians and altitudes, and coordinate-free geometric construction. The construction employs GeoGebra commands such as Segment, and utilizes point objects A, B, X, Y, Y₁, W, Z along with text labels for annotation. It is suitable for high school geometry classes, particularly when teaching triangle construction methods, and serves as an interactive tool for visualizing how given constraints determine a triangle's shape.