Take any triangle. Mark the 3 points which are the intersections of adjacent angle trisectors. No matter what triangle you start with, these 3 points will form an equilateral triangle!
Presentation Suggestions:
Draw a picture and invite students to draw their own triangle on a sheet of paper and follow along.
The Math Behind the Fact:
This is yet another surprising fact from geometry. Can you think of a proof?
How to Cite this Page:
Su, Francis E., et al. “Morley’s Theorem.” Math Fun Facts. <https://www.math.hmc.edu/funfacts>.
Fun Fact suggested by:
Jorge Aarao