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highmath
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How can I prove that If there the only hexagon that his sides equal one to each other then it angles can't be different one from each other?
First of All - thanks!Olinguito said:Indeed it is not true. For example, the hexagon on the left below is equiangular but not equilateral while the one on the right is equilateral but not equiangular.
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You can't because that is not true! Imagine a regular hexagon- all sides the same length and all angle the same, made of sticks "pinned" together- that is, two sticks are held together by a simple pin through holes in the two sticks so that the sticks can rotate around that pin. Now grab two opposite sides and move one left and the other right. The regular hexagon will "warp" into a hexagon still with all sides the same length but non-equal angles.highmath said:How can I prove that If there the only hexagon that his sides equal one to each other then it angles can't be different one from each other?
highmath said:Can you post a picture of equiangular polygon (for example, heagox) that is not equilateral?
I should point out that this is only true for convex polygons, not concave ones.Olinguito said:In general, for any integer $n\geqslant3$, if $n$ is odd, then any $n$-gon is equilateral if and only if it is equilateral …
As written, that statement is true (but vacuous)! From the rest of the thread, it seems that the second "equilateral" should have been "equiangular". The statement would then say "if $n$ is odd, then any $n$-gon is equilateral if and only if it is equiangular". But that statement is not true (as Country Boy pointed out in comment #5). In fact, a child's drawing of a house shows that you can have an equilateral convex pentagon that is not equiangular.Olinguito said:In general, for any integer $n\geqslant3$, if $n$ is odd, then any $n$-gon is equilateral if and only if it is equilateral
Olinguito said:And an equilateral non-equiangular (and non-convex) dodecagon:
Klaas van Aarsen said:This is an equilateral equiangular polygon.
Yes, there are non-regular hexagons. A regular hexagon is defined as a polygon with six equal sides and equal angles, while a non-regular hexagon may have sides and angles of different lengths and measures.
The main difference between a regular and non-regular hexagon is the equality of its sides and angles. A regular hexagon has six equal sides and equal angles, while a non-regular hexagon may have sides and angles of different lengths and measures.
No, a non-regular hexagon cannot have all its angles equal. A regular hexagon is the only type of hexagon with equal angles. A non-regular hexagon will have at least one angle that is different from the others.
There are an infinite number of non-regular hexagons. Each non-regular hexagon can have different combinations of side lengths and angle measures, making it unique. Therefore, it is impossible to determine the exact number of non-regular hexagons.
No, a non-regular hexagon cannot have all its sides equal. A regular hexagon is the only type of hexagon with equal sides. A non-regular hexagon will have at least one side that is different from the others.