# In an equilateral triangle ABC, points M, N, K are the midpoints of the sides AB, BC, CA, respectively. Prove that triangle MNK is equilateral

May 31, 2020 | Education

| Consider the triangles AMK, MBN, and NCK.

∠A = ∠B = ∠C (by the property of an equilateral triangle).

AM = MB = BN = NC = CK = KA (by the condition of the problem).

Therefore, the triangles AMK, MBN and NCK are equal (by the first sign).

It follows that MN = MK = KM => the triangle MNK is equilateral (by definition).

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