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

January 30, 2021 | education

| **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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