The Cinderella sketch above simulates how one can experimentally find the median of a carboard triangle by pinning it at one of its vertices, and letting it loose to swing freely, then the median (or 'balance line') will align with a vertical plumb line. By pinning the triangle at the other two vertices, the other two medians can be found, and the intersection of the three medians then gives us the centroid ('balancing point') of the whole triangle.
Instructions: Ensure that you first press the TURN ON GRAVITY HARDWARE button on the bottom right. Next press the PLAY button on the bottom left to start. Then press in succession, the STEP 1, STEP 2 and STEP 3 buttons. After the triangle and plumb line has come to rest you can also drag the vertices of the triangle or the plumb line. Press the STOP button to reset.
Download the Cinderella sketch above at Finding Triangle Median and Centroid and use it with the dynamic geometry software Cinderella (free to download) or view the video clip below.
Video Clip
Since the Cinderella sketch above is based on Java, it is unfortunately not likely to run any more on newer computers & new browsers. However, here is a video clip illustrating the sketch:
(Click on the pic below to navigate to & activate the clip on YouTube)
Rethinking Proof activity
An online activity from my Rethinking Proof with Sketchpad book (free to download), with a classroom worksheet and guided proof of the concurrency of the medians is available at: The Center of Gravity of a Triangle.
Ceva's theorem
Explore further how to experimentally find the centroid (balancing point) for a triangle with different weights at the vertices at Experimentally Finding the Centroid of a Triangle with Different Weights at the Vertices, and also how this is a physical representation of Ceva's theorem (1678).
Centroids of a quadrilateral
Now explore further how to balance quadrilaterals interactively at Centroid of Cardboard Quadrilateral, Point Mass Centroid of Quadrilateral and Centroid of Perimeter Quadrilateral.
Watch NASA clip about locating centres of gravity of aircraft
Related Links
Experimentally Finding the Centroid of a Triangle with Different Weights at the Vertices (Ceva)
The Center of Gravity of a Triangle (Rethinking Proof activity, concurrency medians, Ceva))
Balancing Weights in Geometry as a Method of Discovery & Explanation
Three different centroids (balancing points) of a quadrilateral
Investigating Centres of Cyclic & Tangential Quadrilaterals coinciding with their Centroids
Proof of concurrency of medians using Desargues' theorem about perspective triangles
Geometry Loci Doodling of the Centroids of a Cyclic Quadrilateral
A side trisection triangle concurrency
Van Aubel Vertex Centroid & its Generalization
Quadrilateral Balancing Theorem: Another 'Van Aubel-like' theorem
Nine Point Conic and Generalization of Euler Line
Anghel's Hexagon Concurrency theorem (Click on the 'Anghel' button in the sketch)
External Links
Aimssec Lesson Activities (African Institute for Mathematical Sciences Schools Enrichment Centre)
UCT Mathematics Competition Training Material
SA Mathematics Olympiad Questions and worked solutions for past South African Mathematics Olympiad papers can be found at this link.
(Note, however, that prospective users will need to register and log in to be able to view past papers and solutions.)
Free Download
Download the Interactive Geometry Software Cinderella for free from the official site: Cinderella Software.
The software can do physical simulations, and apart from working in Euclidean plane geometry, it can also be used to dynamically explore elliptical and hyperbolic geometry.
Back to "Dynamic Geometry Sketches"
Back to "Student Explorations"
Created with Cinderella by Uli Kortenkamp & slightly modified by Michael de Villiers, March 2009; updated 15 March 2021; 16 March 2024; 26 Nov 2025; 28 Sept 2026.