Explore more: In the interactive sketch below, with P, Q, R, S, T, and U the midpoints of the shown segments, some additional properties of the same geometric configuration are shown. Drag any of A, B or C.
What do you observe? What additional conjectures can you make?
Additional challenge: Can you explain (prove) these further conjectures? What happens if sides are divided into four or more equal parts? Explore!
Read our Dec. 2013 paper "A trisection concurrency: a variation on a median theme" (with Shunmugam Pillay) in the Learning and Teaching Mathematics journal in pdf format (881 kb) or in iBook format (2 MB).
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Created by Michael de Villiers, 6 November 2013, modified 14 November 2015.