To identify the inverse of the given statement, let's follow these steps:
1. Understand the Original Statement:
The original statement is:
```
If a shape has four sides, then it is not a triangle.
```
2. Structure of an Inverse Statement:
The inverse of a statement "If [tex]\( p \)[/tex], then [tex]\( q \)[/tex]" is "If not [tex]\( p \)[/tex], then not [tex]\( q \)[/tex]".
3. Identify [tex]\( p \)[/tex] and [tex]\( q \)[/tex] from the Original Statement:
- [tex]\( p \)[/tex]: A shape has four sides.
- [tex]\( q \)[/tex]: It is not a triangle.
4. Negate Both [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
- Not [tex]\( p \)[/tex]: A shape does not have four sides.
- Not [tex]\( q \)[/tex]: It is a triangle.
5. Form the Inverse Statement:
Combining the negated [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
```
If a shape does not have four sides, then it is a triangle.
```
Hence, the inverse of the given statement "If a shape has four sides, then it is not a triangle" is:
```
If a shape does not have four sides, then it is a triangle.
```
Correct Option:
```
O If a shape does not have four sides, then it is a triangle.
```
