That is incorrect. An equilateral triangle is where ALLthe sides of the triangle are the same length. This results in all three of the internal angles being 60 degrees.
However, a Isosceles triangle only has TWO sides that are the same length. This results in two of the internal angles being the same with and the other angle being a smaller angle to add up to the 180 degrees.
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False. Equilateral triangles are equilateral. All isosceles triangles have two of the sides the same, with the hypotenuse being longer than the other two.
A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).
Sure. That's true of a median in every isosceles triangle, and every median in an equilateral triangle. In fact it is true for any median of any triangle. The two parts may not be the same shapes but they will have the same area. That is why the point where the three medians meet (centroid) is the centre of mass of a triangular lamina of uniform thickness.