First, make an equilateral triangle and label all the points. All the line segments that have a ratio of 1, mark those as congruent and all the line segments that have a ratio of 3, mark those congruent as well. Now, what we can is 3 congruent triangles by SAS, (AMK = BPM = CKP). Then, we take MP, PK, and KM and we know those are congruent because of CPCTC. That means all the sides are equal in the inner triangle which means it is an equilateral triangle.
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