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Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

Uncanny Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Where is a good place to start?
Have you looked at some of the examples on the sheet?
How many different triangles do you think you can draw with the lengths of the two perpendicular and horizontal sides making any total up to $15$? Can you list some? How do you know you can list them all without missing any out?
Have you thought of trying the "family" of triangles with a height of one?
Do you need to draw all the triangles in a family to see if any meet the requirements? How can you tell?


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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NRICH is part of the family of activities in the Millennium Mathematics Project.