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Can you divide an equilateral triangle into exactly 12 congruent triangles? interesting question i haven't yet been able to work on. The sides can be of any length.

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    $\begingroup$ Can you divide any triangle into exactly 4 congruent triangles? $\endgroup$ – Blue Jun 14 '12 at 15:23
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    $\begingroup$ How about first dividing the triangle into 3 congruent triangles by joining the centre (centroid) to the 3 vertices, and then dividing the 3 smaller triangles into 4 congruent triangles the obvious way? $\endgroup$ – Old John Jun 14 '12 at 15:23
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Here is a hint for one way to do it:

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  • $\begingroup$ "A hint"? Very nice answer. +1 $\endgroup$ – DonAntonio Jun 15 '12 at 3:55

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