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In the figure below, equilateral triangles ABC_{1} and A_{1}BC are drawn on the sides of a triangle ABC. If B_{1}, A_{2}, and C_{2} are the midpoints of AC, BC_{1}, and A_{1}B, respectively, prove that the triangle A_{2}B_{1}C_{2} is equilateral.

#TriangleSurprise! When we build equilateral triangles off 2 sides of ANY TRIANGLE, another equilateral triangle surprisingly emerges! 😮 Why does this occur? 🤔Source: @gogeometry. Created with @geogebra: https://t.co/lTfrId4Hik. #geometry #math #MTBoS #ITeachMath #maths #EdTech pic.twitter.com/CUeFSPKsYy— Tim Brzezinski (@Brzezinski_Math) August 16, 2019

#TriangleSurprise! When we build equilateral triangles off 2 sides of ANY TRIANGLE, another equilateral triangle surprisingly emerges! 😮 Why does this occur? 🤔Source: @gogeometry. Created with @geogebra: https://t.co/lTfrId4Hik. #geometry #math #MTBoS #ITeachMath #maths #EdTech pic.twitter.com/CUeFSPKsYy

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Post or view a solution to the problem 1218 Last updated: May 26, 2016