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Is it possible for a hexagon to be equiangular but not equilateral? Prove your answer.

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No, this is not possible. The total sum of angles in a hexagon is 720 degree and each angle is a measure of 120 degree. Such a hexagon is called a regular hexagon. By increasing or decreasing the length of any side of hexagon, it will consequently affect the corresponding angle and hence the hexagon will be no more an equiangular hexagon.

The attached images clarify the above statement.

Is it possible for a hexagon to be equiangular but not equilateral? Prove your answer-example-1
Is it possible for a hexagon to be equiangular but not equilateral? Prove your answer-example-2
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