The Arithmetic Average of Altitudes From Vertices of a Parallelogram to a Straight Line: A Sketch and Proof

Abstract

The author illustrates a method for motivating mathematical generalization with students using GeoGebra. Building on student interest in amusement parks, the author connects an initial question about Ferris wheel riders to general quadrilaterals in the plane. In a culminating activity, students construct a rigorous algebraic proof confirming their initial conjectures.