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
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).
Now explore further how to balance quadrilaterals interactively at Centroid of Cardboard Quadrilateral and Point Mass Centroid of 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
The Center of Gravity of a Triangle (Rethinking Proof activity)
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
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Created with Cinderella by Uli Kortenkamp & slightly modified by Michael de Villiers, March 2009; updated 15 March 2021 to WebSketchpad; updated 16 March 2024; 26 Nov 2025.