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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 D, E, and F are the midpoints of BC, AB, and A_{1}C_{1}, respectively, prove that the triangle DEF is equilateral.

#Euclidean #Geometry Problem 1220: #Equilateral #Triangles Midpoints, 60 Degrees, Congruence at https://t.co/YHf7QO9wD9 pic.twitter.com/lOD5cI7Qir— Antonio Gutierrez (@gogeometry) August 19, 2017

#Euclidean #Geometry Problem 1220: #Equilateral #Triangles Midpoints, 60 Degrees, Congruence at https://t.co/YHf7QO9wD9 pic.twitter.com/lOD5cI7Qir

#Math Enthusiasts: Why is THIS always true for ANY TRIANGLE? (T/Y 2 @gogeometry). https://t.co/UEta0sjslV @geogebra #mathchat #geometry pic.twitter.com/HfXKnmZchX— Tim Brzezinski (@dynamic_math) August 19, 2017

#Math Enthusiasts: Why is THIS always true for ANY TRIANGLE? (T/Y 2 @gogeometry). https://t.co/UEta0sjslV @geogebra #mathchat #geometry pic.twitter.com/HfXKnmZchX

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Post or view a solution to the problem 1220 Last updated: Jun 1, 2016