In which triangle is any median bisector and height, and why?

Any median is the bisector and the height in an equilateral triangle.

Since the median drawn from the top of the isosceles triangle to the base is the bisector and the height, then in an equilateral triangle, from whatever vertex we draw the median, the sides outgoing from this vertex are equal. This means that a triangle has the same properties as an isosceles triangle.



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