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Proving a Polygon is Regular

Is the polygon formed by connecting the points (1,0) (5,1) (4,5) and (0,4) regular?

Remember: In Euclidean Geometry, regular means that all of the sides and angles are equal.

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$AB = \sqrt{(0-4)^2+(4-5)^2}=\sqrt{17}$

$BC = \sqrt{(4-5)^2+(5-1)^2} = \sqrt{17}$

$CD = \sqrt{(1-5)^2+(4-0)^2}=\sqrt{17}$

$AD = \sqrt{(0-1)^2 +(4-0)^2} = \sqrt{17}$