Prove that the distances from the vertices of an equilateral triangle to the lines containing the opposite sides are equal

The distance from the top to the opposite side is the perpendicular.
Let’s designate this equilateral triangle ABC, draw the heights: AH, BK, CM.
Consider right-angled triangles ABK, AСН, BСК, in them:
– hypotenuse (side of an equilateral triangle) AB = BC = AC.
– ∠ A = ∠ B = ∠ C = 60 ° (angles of an equilateral triangle).
Received one of the signs of equality of right-angled triangles – by hypotenuse and acute angle.
Equality of triangles implies equality of all sides and angles.
AH = BK = CM.
Q.E.D.