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  1. Is there any triangle that can be cut into 5 mutually congruent pieces? If the answer is "yes" how does one characterize such triangles? What if we restrict the pieces to be convex?

  2. Is there any convex pentagon that can be cut into 3 mutually congruent pieces?

Nandakumar R
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    Don't just paste the question and yeet off. Show us the work you tried, what you're confused on, ect. This isn't enough detail at all. – Caedmon Jan 13 '22 at 16:54
  • You may find this question interesting. It shows a dissection of an equilateral triangle into 5 congruent pieces, though the pieces are not connected subsets of the plane. – Jaap Scherphuis Jan 13 '22 at 17:03
  • Thanks Jaap Scherphuis. The dissection you pointed at is certainly interesting. But I was looking for connected pieces although I didn't spell it out explicitly in the question. – Nandakumar R Jan 13 '22 at 17:50
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    A right triangle with legs in the ratio 2:1, maybe? – Oscar Lanzi Jan 14 '22 at 01:08

1 Answers1

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drawing

Worth a thousand words, they say.

Ivan Neretin
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  • thanks very much. i had indeed overlooked some basic possibilities while trying to dissect pentagons and hence asked the question. but then that is math! – Nandakumar R Jan 14 '22 at 12:20