Equilateral linkage

Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?

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Yes it is.

Solution by Matthew Arcus.

A simpler way: HA is a 120° rotation of CB, so comparing the yellow and black dashed segments, KA must be a 120° rotation of JK.

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