Triangle Dissections We all know that
you can cut (or ‘dissect’) a square into 4 equal, but smaller, squares.
These are ‘selfsimilar’ to the original square  the same shape, but
a different size. You
can do a similar thing to create a diagram with 9 smaller squares. Can
you do the same thing, dissecting any triangle into 4 smaller selfsimilar
triangles, using a similar approach ? Problem Set 1 Starting
with the rather special triangles shown below  the 30°, 60°, 90° triangle
that is half an equilateral triangle, and the ‘halfdomino’ triangle  there
are 2 nice challenges along similar lines ... :
A
Can you show how to dissect the first into just 3 smaller selfsimilar
triangles ? B
Can you show how to dissect the second into 5 smaller selfsimilar
triangles ? Problem Set 2 Starting
with an equilateral triangle, can you show how to dissect it into : C
12 identical triangles (not necessarily equilateral) D
13 equilateral triangles (not necessarily all the same size) E
14 triangles of the same area (but not necessarily the same shape)
F
15 equilateral triangles (not necessarily all the same size) G
16 equilateral triangles.
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