Similar Triangles

'Sort out the triangles so you can work out the missing lengths!' 

There are lots of things that we can do with the 24 triangles used in this activity (download and print below)! The simplest way to describe this activity is that you have to find the missing lengths on the triangles. The catch is that you are not allowed to measure any lengths or any angles. The only tool you have is to compare the angles in the triangles with each other! Perhaps you'll start by trying to group the triangles together in different ways to establish what common properties they might have. Then you will need to use some proportional reasoning to see if you can deduce the missing lengths! Once you have done this you can use these triangles to work with Pythagoras theorem and trigonometry as well!


This activity revolves around this  Set of 24 triangles that need to be printed and cut out. One set per group is required. Some structure can be added to this activity with this  Similar Triangles activity sheet. So as not to give too much away on this page there are some  Similar triangles teacher notes to go over the key points of this activity.



  • Triangles are prepared in advance or students quickly cut them out at the start of the lesson.
  • VERY IMPORTANT - students must not use rulers or protractors.
  • Students are asked to classify the triangles in any way they see fit and justify their choices.
  • There can be some whole class discussion about the chosen classifications.
  • Students are asked to group the triangles in such a way that they can work out what the missing lengths of the triangles are.
  • A number of questions can follow about the different scale factors of enlargement between the groups of similar triangles.
  • There is possible extension into Pythagoras's theorem and trigonometry.
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