One Half Perimeter vs. Sum of Altitudes

This GeoGebra example dynamically compares one half of a triangle's perimeter with the sum of its three altitudes. It visually demonstrates the inequality relationship between these two quantities as the triangle changes shape. Core concepts include triangle perimeter, altitude, area, and inequality reasoning. The construction uses commands such as Segment, Line, OrthogonalLine, Intersect, and Polygon to build the triangle and its altitudes, with sliders or draggable points for interactive exploration. Suitable for middle and high school geometry classes to investigate when the half-perimeter is greater than, equal to, or less than the sum of altitudes, fostering inquiry into geometric inequalities.