What shapes don't have lines of symmetry besides circles and ovals?
Circles and Ovals DO have lines of symmetry: a circle has an
infinite number of them (each is a diameter of the circle) and an
oval (ellipse) has two (one along the major axis, one along the
minor axis).
Shapes which have no lines of symmetry are irregular ones, eg
scalene triangles, along with most parallelograms (ie
parallelograms which are not rhombuses) and non-isosceles
trapezia.
Some irregular shapes can have lines of symmetry, eg irregular
octagons can have 1, 2 or 4 lines of symmetry as well as no lines
of symmetry, unlike a regular octagon which [always] has 8 lines of
symmetry.