Q: Do some shapes have no lines of symmetry?

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not all shapes have lines of symmetry. one example is a triangle.

A square has 4 lines of symmetry

trianglessquaresrectanglesgeneral starsoctagonshexagonspentagons

Three dimensional shapes, generally, don't have lines of symmetry, but a circle has an infinite number is symmetry lines. 3D shapes also don't have rotational symmetry either, but a circle has an infinite number of that as well.

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.

Related questions

not all shapes have lines of symmetry. one example is a triangle.

No. Asymmetric shapes do not have any lines (or planes) of symmetry.

no

A square has four lines of symmetry.

Ellipses and non-square rectangles have two lines of symmetry.

A square has 4 lines of symmetry

trianglessquaresrectanglesgeneral starsoctagonshexagonspentagons

Three dimensional shapes, generally, don't have lines of symmetry, but a circle has an infinite number is symmetry lines. 3D shapes also don't have rotational symmetry either, but a circle has an infinite number of that as well.

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.

Most shapes do not have lines of symmetry so why should it come as a surprise that a parallelogram has none?

Equilateral triangle.

sircle