Dynamic Geometric Demonstration of Ceva's Theorem

This example demonstrates Ceva's Theorem, which states that in triangle ABC, three cevians AD, BE, and CF drawn from vertices to opposite sides are concurrent if and only if (BD/DC)·(CE/EA)·(AF/FB) = 1. The GeoGebra applet dynamically constructs the triangle, intersection points, and segments, using vectors and ratio calculations to illustrate the geometric significance of the theorem. Users can drag the vertices of the triangle in real time to observe how the individual ratios and their product change dynamically. As points are moved, the applet continuously recalculates the segment ratios and displays the product (BD/DC)·(CE/EA)·(AF/FB), allowing students to verify that the product remains equal to 1 precisely when the three cevians are concurrent. This interactive exploration provides an intuitive understanding of the deep connection between intersection ratios of line segments inside a triangle and the concurrency property of those segments. The applet is designed to help students develop geometric intuition and reinforce their proof-based understanding of Ceva's Theorem through hands-on experimentation. By manipulating the configuration and observing the invariant multiplicative relationship among the ratios, learners gain insight into why the theorem holds and how it generalizes to various configurations, including cases where the point of concurrency lies outside the triangle.