To construct a quadrangle EFGH having three equal sides EF=FG=GH, whose known are the three middles {B,A,C} of the equal sides.
Triangle ABC is constructible. From it also point J, defined as intersection point of the medial lines of AB, AC. Then I is constructible as symmetric of J w.r. to A. By drawing parallels from I to the aforementioned medials we obtain the parallelogram IFJG, of which FG is the other diagonal.
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Quadrangle construction ![[0_0]](QuadConstruction_files/QuadConstruction_0_0_0.png)