“Possible Isosceles”: Because statements 1 and 2 are practically the same, could either of them also refer to an equilateral triangle?

Question

Because statements 1 and 2 are practically the same, could either of them also refer to an equilateral triangle?

Answer

You're actually completely correct here. The only piece of the puzzle that you are missing is that an equilateral triangle is a special type of isosceles triangle—so by saying that ABC could be equilateral or isosceles, you are in fact confirming that it has to be some type of isosceles triangle.

The reason this is true is that for a triangle to be considered isosceles, it has to have at least 2 equal sides. An equilateral triangle has 3 equal sides—meaning that it is also an isosceles triangle, just a special case. However, not all isosceles triangles are equilateral!

Think of it kind of like squares and rectangles. A square is a special type of rectangle in which all sides are equal length—therefore all squares are rectangles, but not all rectangles are squares. This is the same for triangles—all equilateral triangles are isosceles, but not all isosceles triangles are equilateral!

Link

http://gmat.magoosh.com/questions/1024