Impossible Triangles

Can these triangles exist?

The main thrust of this activity is easily explained - What reasoning can you use to decide if these triangles can exist or not? [1] This is an alternative way to apply what you know about triangle geometry. Pythagoras's theorem, SOHCAHTOA (right-angled trigonometry), Sine rule, Cosine rule and more can all be used to reason one way or another. The whole point is for students to enter in to discussion with each other! There are lots of ways to approach this task most of which revolve around the notion of 'IF this is true, THEN this must be true... Good Luck!


The Impossible Triangles can be printed and screen shots are included below. Teachers can see the solutions and read a bit about the activity on the  Teacher Notes  for Impossible Triangles.


  • I think this activity works best without any introduction from the teacher or clues about how to go about it. Simply hand out the worksheet and ask students to say which of the triangles can exist.
  • Alternatively, teachers might choose to start with an example as a whole class and discuss.
  • Once finished, you might choose to split the class in two and have a little competition where teams take turns to pick a letter. They score a point if they have correctly judged it possible or not!


  • 1. Assume that all lengths are rounded to the nearest whole number
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