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BFH is equilateral if ABCD is a 120-60 rhombus and DFGH is #

Source: 2023 Mathematics Regional Olympiad of Mexico West P5

October 21, 2024
geometryrhombusEquilateralparallelogram

Problem Statement

We have a rhombus ABCDABCD with ∠BAD=60∘\angle BAD=60^\circ. We take points F,H,GF,H,G on the sides AD,DCAD,DC and the diagonal ACAC, respectively, such that DFGHDFGH is a parallelogram. Prove that BFHBFH is equilateral.
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