What kinds of symmetry do an equilateral and an isosceles triangle have?

An equilateral triangle has six symmetries, and an isosceles triangle has two. An isosceles triangle has a single axis of symmetry, the perpendicular bisector of the non-congruent side. This is a reflection symmetry. An equilateral triangle has rotational symmetry as well as reflection symmetry. It is invariant under rotations by 120 degrees.