Create a symmetrical pattern - Geometry (Shape) by URBrainy.com - Free Printable

Problem Description:

The task is to create symmetrical patterns by completing the given half-patterns. The goal is to reflect the existing red squares across the vertical blue line to make each pattern symmetrical.

Solution Approach:

1. Understand Symmetry: Symmetry means that one side of the pattern is a mirror image of the other side with respect to the blue line.
2. Identify the Blue Line: The blue vertical line acts as the axis of symmetry. Everything on the left side of this line should have a corresponding reflection on the right side.
3. Reflect Each Red Square:
- For each red square on the left side of the blue line, draw an identical red square on the right side at the same distance from the blue line.
- Ensure that the reflected squares maintain the same relative position as their counterparts on the left.

Step-by-Step Solution:

#### Pattern 1:
- Left Side: Two red squares in the second row.
- Reflection: Place two red squares in the same positions on the right side of the blue line.
- Completed Pattern:
```
| | | | |
| | | | |
| R | R | R | R |
| | | | |
```

#### Pattern 2:
- Left Side: Three red squares: one in the first row, one in the second row, and one in the third row.
- Reflection: Place three red squares in the same positions on the right side of the blue line.
- Completed Pattern:
```
| | | | |
| R | | | R |
| R | | | R |
| R | | | R |
```

#### Pattern 3:
- Left Side: Four red squares forming an "L" shape.
- Reflection: Reflect the "L" shape across the blue line to form a mirrored "L" shape on the right.
- Completed Pattern:
```
| | | | |
| R | R | R | R |
| R | | | |
| R | R | | |
```

#### Pattern 4:
- Left Side: Two red squares in the second row.
- Reflection: Place two red squares in the same positions on the right side of the blue line.
- Completed Pattern:
```
| | | | |
| | | | |
| R | R | R | R |
| | | | |
```

#### Pattern 5:
- Left Side: Three red squares forming a diagonal line from the top-left to the bottom-left.
- Reflection: Reflect the diagonal line across the blue line to form a mirrored diagonal line on the right.
- Completed Pattern:
```
| | | | |
| R | | | R |
| | R | R | |
| | | | |
```

#### Pattern 6:
- Left Side: Four red squares forming a block in the bottom-left corner.
- Reflection: Reflect the block across the blue line to form a mirrored block on the right.
- Completed Pattern:
```
| | | | |
| | | | |
| | | | |
| R | R | R | R |
```

Final Answer:

Here are the completed symmetrical patterns:

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

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

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

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

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

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

Thus, the final answer is:

\boxed{
\begin{array}{c}
\text{Pattern 1:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
& & & \\
\hline
R & R & R & R \\
\hline
& & & \\
\hline
\end{array} \\
\text{Pattern 2:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
R & & & R \\
\hline
R & & & R \\
\hline
R & & & R \\
\hline
\end{array} \\
\text{Pattern 3:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
R & R & R & R \\
\hline
R & & & \\
\hline
R & R & & \\
\hline
\end{array} \\
\text{Pattern 4:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
& & & \\
\hline
R & R & R & R \\
\hline
& & & \\
\hline
\end{array} \\
\text{Pattern 5:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
R & & & R \\
\hline
& R & R & \\
\hline
& & & \\
\hline
\end{array} \\
\text{Pattern 6:} \\
\begin{array}{|c|c|c|c|}
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
R & R & R & R \\
\hline
\end{array}
\end{array}
}