When an object can be shifted, say to the left or right, and still remains the same; this is an example of what time of symmetry

Is it bilateral symmetry

bilateral symmetry is a mirror image along a line, so each side is NOT the same, but reversed.

shifting left to right remaining the same is translational symmetry http://en.wikipedia.org/wiki/Translational_symmetry

The type of symmetry you are describing is called "translational symmetry." Translational symmetry refers to the property of an object or pattern that remains unchanged when it is shifted or translated in a particular direction. In your case, when an object can be shifted to the left or right and still appears the same, it exhibits translational symmetry along the horizontal axis.

To identify translational symmetry in an object, you can follow these steps:

1. Observe the object: Look for any patterns, shapes, or designs present in the object.
2. Shift the object: Try shifting the object horizontally, either to the left or right.
3. Compare the original and shifted versions: Analyze whether the object remains the same after the shift. If the object looks unchanged, it demonstrates translational symmetry.

Keep in mind that translational symmetry can also occur in other directions, such as vertically or diagonally. The key is to identify whether the object remains identical after being shifted in a particular direction.