Two congruent equilateral triangles
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
and
![A'B'C'](/media/m/5/3/d/53d1d147ad89bd52a7038ce57a0957ef.png)
in the plane are given. Show that the midpoints of the segments
![AA',BB', CC'](/media/m/7/2/3/72331f827e71769e76a0392f255d01e3.png)
either are collinear or form an equilateral triangle.
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Two congruent equilateral triangles $ABC$ and $A'B'C'$ in the plane are given. Show that the midpoints of the segments $AA',BB', CC'$ either are collinear or form an equilateral triangle.