Check a biology textbook - I reckon it's lateral (left-to-right) symmetry, as the body does not have the cylindrical shape that would qualify it for radial symmetry.

Symmetry is important in an organizational sense. It makes a difference in biology, mineralogy and physics. Its importance also touches on physical laws.

Symmetry in biology is the balanced distribution of duplicate body parts or shapes. The body plans of most multicellular organisms exhibit some form of symmetry, either radial symmetry or bilateral symmetry or "spherical symmetry". A small minority exhibit no symmetry (are asymmetric).

Animals with radial body symmetry display a regular arrangement of body parts around a central axis, usually in a circular pattern. Creatures such as jellyfish and sea anemones have radial symmetry.

Dogs have no lines of symmetry. They're never completely equal on both sides. No creatures are.

However, in terms of biology, dogs, like all vertebrates, have bilateral symmetry. This means they have symmetry across one plane (known as the sagittal plane, and directly down the centre of their body), which means one side of their body approximately mirrors the other side. Thus, they have a single line of symmetry.