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The following shape is has the proportions of a square attached to a similar square divided diagonally - A square and a half, if you may.

enter image description here

The puzzle is to dissect the shape into 4 congruent pieces.

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

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    $\begingroup$ Can the pieces be mirror images of each other? $\endgroup$ – Aza May 17 '14 at 17:52
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    $\begingroup$ Yes, absolutely. But extra points if they aren't ;). $\endgroup$ – John Bupit May 17 '14 at 17:57
  • $\begingroup$ they must be congruent then $\endgroup$ – ratchet freak May 17 '14 at 17:58
  • $\begingroup$ Yes. I think it's more clear now. I was looking to avoid a mathematical term, though. $\endgroup$ – John Bupit May 17 '14 at 18:03
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    $\begingroup$ For future reference, LiveGeometry is a wonderful tool. $\endgroup$ – Aza May 17 '14 at 18:15
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The first thing to do is divide the figure into a number of sections which is a multiple of four. The easiest way to do this is to split it up into smaller triangles:

triangle division

Note that there are now 12 sections, which divides into sections of 3. Three triangles forms a square and a smaller triangle. We know, as a result, that a square must go here (another way to do this is that the triangle in the corner must be part of a shape of three parts):

enter image description here

From this, it becomes clear where the rest of the divisions lie. The remaining triangle, as part of the triangular section, must be part of a set of three, so as a result, we know that it is as follows:

enter image description here

The rest of the divisions are simple:

enter image description here

And, as a side note, for future reference, LiveGeometry is a wonderful little tool.

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  • $\begingroup$ This one's way better than mine. $\endgroup$ – Joe Z. May 17 '14 at 18:09
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    $\begingroup$ @JoeZ. We have the same solution, though, to be fair! $\endgroup$ – Aza May 17 '14 at 18:11
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    $\begingroup$ @John I won't choose for you, since that would be incredibly biased, but the canonical advice from Meta Stack Exchange on this topic is available in this FAQ answer under "Which answer should I choose?" $\endgroup$ – Aza May 17 '14 at 18:17
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    $\begingroup$ @JohnBupit An answer with an explanation is always more useful than one with just the answer. (Not to say anything bad about Joe's answer; just in general.) That said, anyone can upvote either and your checkmark is yours to place :) $\endgroup$ – WendiKidd May 17 '14 at 21:42
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    $\begingroup$ I would personally recommend you accept this answer (which you seem to have done, congrats). $\endgroup$ – Joe Z. May 18 '14 at 15:05
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The solution appears as follows:

solution to the puzzle

It's a bit rough, but it shows the right places to cut the shape.

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