yes
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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.
Yes. In this case, the isosceles triangle would more specifically be an equilateral triangle - this can be considered a special case of an isosceles triangle.
an equilateral triangle
No, isosceles and equilateral are two separate types of triangles. Isosceles triangles have only two congruent sides, while all three sides of an equilateral triangle are congruent.
No but it is possible for it to be an isosceles triangle with angles of 45, 45 and 90 degrees