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Let's draw an equilateral triangle knowing the side.

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This is supposed to be the side of our triangle.

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This is point A, this is point B.

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And we have to find a point C whose distance to point A is AB, the same, and to point B also the same.

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The distance must be the same in the three positions.

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So if we point the needle of the compass in B and we make an arch with the radius AB,

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all those points have the same distance to B than at A. And if we do the same,

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pointing the needle of the compass on A, okay, all those points have the same distance to A

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than B. So we will find a third point at the same distance here in C, and we will

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obtain an equilateral triangle when we join the points. Also, yes, because the

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geometry is a kind of magic, we will have that all the angles of this triangle

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measure the same.