Triangle Dissections
We all know that
you can cut (or �dissect�) a square into 4 equal, but smaller, squares.
These are �self-similar� 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 self-similar
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 �half-domino� triangle - there
are 2 nice challenges along similar lines ... :
A
Can you show how to dissect the first into just 3 smaller self-similar
triangles ?
B
Can you show how to dissect the second into 5 smaller self-similar
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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