# Point M is marked inside an equilateral triangle ABC so that AM = BM. Prove that the beam CM

Point M is marked inside an equilateral triangle ABC so that AM = BM. Prove that the beam CM is the bisector of the angle ACB.

We are given an equilateral triangle.
CM is the median in this triangle, since it divides the base into two equal parts, because AC = BC;
The main property of an isosceles triangle can be attributed to an equilateral triangle:
in an isosceles triangle, the median lowered to the base is also the bisector and height.
Since all sides in this triangle are equal, then any median is also a bisector and a height.
That is, CM is a bisector that divides angle C into two equal angles.

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