No, symmetrical objects are not identical to each other because, by the provided definition, they possess different orientations, even if their shape and size are the same.
Understanding Symmetry in Objects
According to the provided definition, two objects are symmetrical if they are of same shape, same size and one object has a different orientation from the other. This definition highlights a specific relationship between two distinct objects. It implies that if you have two objects that are mirror images of each other (like your left and right hand) or one is simply a rotated version of the other, they can be considered symmetrical.
Key characteristics from this definition:
- Same Shape: Both objects must have the exact same form.
- Same Size: Both objects must occupy the same amount of space.
- Different Orientation: This is the crucial distinguishing factor. One object is positioned differently in space relative to the other.
The Concept of Identical Objects
In contrast, "identical" implies that two or more objects are exactly alike in every single detail. This includes not just their shape and size, but also their precise orientation, position in space, material composition, and any other intrinsic or extrinsic properties. If two objects are identical, they are indistinguishable from one another if you were to swap their places.
Why Symmetrical Objects Are Not Identical
The core reason why symmetrical objects, as defined, are not identical lies in the requirement of different orientation. For objects to be truly identical, their orientations must also be the same.
Consider the following distinctions:
- Symmetrical Objects: While they share shape and size, their differing orientations mean they are not superimposable without a transformation (like rotation or reflection).
- Identical Objects: They are perfectly superimposable, meaning they would perfectly overlap if one were placed exactly on top of the other, without any need for rotation or reflection.
Here's a quick comparison:
| Feature | Symmetrical Objects (as defined) | Identical Objects |
|---|---|---|
| Shape | Same | Same |
| Size | Same | Same |
| Orientation | Different | Same |
| Relationship | One is a transformed version (e.g., rotated, reflected) of the other | Exactly the same in all aspects, perfectly superimposable |
Practical Examples
To illustrate this, consider these examples:
- Left Hand vs. Right Hand: Your left hand and your right hand are symmetrical. They have the same shape and size, but they are mirror images of each other (different orientation) and cannot be perfectly superimposed. You cannot fit a left glove on a right hand perfectly. Therefore, they are symmetrical but not identical.
- Two Chess Rooks: Imagine two chess rooks that are exactly the same make and model.
- If one rook is standing upright and the other is lying on its side, they are symmetrical according to the definition (same shape/size, different orientation) but clearly not identical in their current state.
- If both rooks are standing upright in the exact same orientation and position, then they would be considered identical.
In essence, while symmetry describes a powerful equivalence in form and size, the difference in orientation prevents symmetrical objects from being truly identical.
