Symmetry 2 - Geometry (Shape) by URBrainy.com - Free Printable

To solve the problem of completing the symmetrical patterns using a mirror line, we need to reflect the given part of each pattern across the mirror line. Here's how to approach it step by step:

---

Understanding Symmetry

- A mirror line (or axis of symmetry) divides a shape into two parts that are mirror images of each other.
- To complete the pattern, we need to replicate the existing red squares on the opposite side of the mirror line, ensuring they are mirrored correctly.

---

Step-by-Step Solution

#### Pattern 1:
- Mirror Line: Vertical
- Given Part: Red squares are on the left side of the mirror line.
- Reflection: Copy the red squares from the left side to the right side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| |
| R |
| |
```

#### Pattern 2:
- Mirror Line: Vertical
- Given Part: Red squares are on the right side of the mirror line.
- Reflection: Copy the red squares from the right side to the left side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| |
| R R R |
| |
```

#### Pattern 3:
- Mirror Line: Vertical
- Given Part: Red squares are on the left side of the mirror line.
- Reflection: Copy the red squares from the left side to the right side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R |
| R R R |
| R |
| |
```

#### Pattern 4:
- Mirror Line: Vertical
- Given Part: Red squares are on the right side of the mirror line.
- Reflection: Copy the red squares from the right side to the left side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| R R R |
| R R R |
| |
```

#### Pattern 5:
- Mirror Line: Vertical
- Given Part: Red squares are on the right side of the mirror line.
- Reflection: Copy the red squares from the right side to the left side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| R R R |
| R R R |
| |
```

#### Pattern 6:
- Mirror Line: Vertical
- Given Part: Red squares are on the left side of the mirror line.
- Reflection: Copy the red squares from the left side to the right side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| R R R |
| R R R |
| |
```

#### Pattern 7:
- Mirror Line: Vertical
- Given Part: Red squares are on the right side of the mirror line.
- Reflection: Copy the red squares from the right side to the left side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| R R R |
| R R R |
| |
```

#### Pattern 8:
- Mirror Line: Vertical
- Given Part: Red squares are on the left side of the mirror line.
- Reflection: Copy the red squares from the left side to the right side, maintaining the same distance from the mirror line.
- Completed Pattern:
```
| R R R |
| R R R |
| R R R |
| |
```

---

Final Answer

The completed patterns are as follows:

1.
```
| R R R |
| |
| R |
| |
```

2.
```
| R R R |
| |
| R R R |
| |
```

3.
```
| R |
| R R R |
| R |
| |
```

4.
```
| R R R |
| R R R |
| R R R |
| |
```

5.
```
| R R R |
| R R R |
| R R R |
| |
```

6.
```
| R R R |
| R R R |
| R R R |
| |
```

7.
```
| R R R |
| R R R |
| R R R |
| |
```

8.
```
| R R R |
| R R R |
| R R R |
| |
```

Thus, the final answer is:
\boxed{
\begin{array}{c}
\text{Patterns completed as shown above.}
\end{array}
}