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An Introduction to Irrational Numbers

Equal Equilateral Triangles

Stage: 4 Challenge Level: Challenge Level:1

Full screen version
This text is usually replaced by the Flash movie.

Click on the green or yellow triangles to get a copy.
Drag the triangle by its interior to the required position and drag any vertex to rotate it.

  • Can you make a regular hexagon using only yellow triangles ?

  • Can you make a regular hexagon using only green triangles ?

  • Can you make a regular hexagon from yellow triangles that is the same size as a regular hexagon made from green triangles ?

Did that tell you something about yellow and green triangles, about how they relate to each other ?

  • Can you make an equilateral triangle from yellow triangles ?
  • Can you make an equilateral triangle from green triangles ?
  • Can you make an equilateral triangle from yellow triangles that is the same size as an equilateral triangle made from green triangles ?

Hold down SHIFT and click here to listen to the audio file . The audio will then start in a new window.

Also, if you wish, follow the 'Hint' tab at the top of this screen for more help.

And when you've got inside this problem and started to feel your way around, please do take a look at Impossible Triangles? - it's the perfect follow on. There's even a video to watch to make getting started easy.



The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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