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I'm pretty sure it's common knowledge that a shape with all the interior angles being the same means the lengths of the sides must be the same, but I want to make absolutely sure I haven't got mixed up. If I had the length of one side, and knew all the interior angles to be equal, could i deduce from that that the rest of the sides are the same length as the one I know?

Dalekcaan1963
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    "...a shape with all the interior angles being the same means the lengths of the sides must be the same", definitely not. Are all rectangles the same? – Edu Oct 17 '16 at 11:11
  • Edit: specifically odd numbered sides shapes such as pentagons – Dalekcaan1963 Oct 17 '16 at 11:15
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    Similar triangles. – JP McCarthy Oct 17 '16 at 11:18
  • Would it be true that a pentagon with equal interior angles and three equal sides (the top two and the base) must be equilateral, since the other two sides can't lengthen or shorten without affecting the length of the base? – Dalekcaan1963 Oct 17 '16 at 11:47

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This is a simple counterexample

pentagon

Henry
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  • Is it possible to have equal sides but different angles ? –  Apr 13 '18 at 12:44
  • @ZahraaKhalife Very easily: build a pentagon (or other polygon with $n>3$) with equal sides and and with hinges at the vertices - it is very easy to change the angles – Henry Apr 13 '18 at 13:38
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No, this is not true. For example, a rectangle. Or, imagine a stop sign split right down the middle and the two halves moved out left and right. The angles are unchanged, but two of the sides are now longer.

Edited after question edited: This is true for odd-numbered sided polygons as well. For example, a pentagon with a side at the bottom can be shortened and pulled downward while preserving the angle measures.

turkeyhundt
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