Which shape has line of symmetry but not rotational symmetry?

Answer 1

There are infinitely many such shapes:

1. Take any odd-sided regular polygon
2. Move one vertex away from the side opposite it in a perpendicular direction any distance you like.

The resulting shape has one line of symmetry (from the vertex moved to the centre of the opposite side) and no rotational symmetry.

Done to an equilateral triangle (a regular "3-agon") this creates an isosceles triangle.