Block Symmetry Worksheet 11: Use the lines of symmetry to complete the missing patterns.

Let's solve the Block Symmetry Worksheet 11 step by step.

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🔍 Objective:

Use the lines of symmetry to complete each pattern. For each grid, you are given a partial pattern and a line (or lines) of symmetry. You need to reflect the shaded blocks across the line(s) to complete the full symmetric design.

We’ll go through each of the six grids one by one.

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✔ Grid 1: Horizontal Line of Symmetry

- Line: A horizontal line divides the grid into top and bottom halves.
- Given: The top half has shaded squares.
- Task: Reflect those shaded squares across the horizontal line to fill the bottom half.

#### Steps:
- For every shaded square in the top half, find its mirror image in the bottom half (same column, mirrored row).
- Example: If a square is at (row 2, col 3), its reflection is at (row 6, col 3) assuming 8 rows total.

✔ Complete the bottom half so it mirrors the top.

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✔ Grid 2: Vertical Line of Symmetry

- Line: A vertical line down the middle.
- Given: Left side has shaded squares.
- Task: Reflect each shaded square across the vertical line to the right side.

#### Steps:
- For each shaded square on the left, draw a shaded square at the same distance from the line on the right.
- Example: If a square is at (row 4, col 2), its mirror is at (row 4, col 6) if the center is between col 4 and 5.

✔ Fill the right side as a mirror of the left.

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✔ Grid 3: Diagonal Line (Top-Left to Bottom-Right)

- Line: Diagonal from top-left to bottom-right (like \).
- Given: Shaded squares on one side of the diagonal.
- Task: Reflect each shaded square across this diagonal.

#### Reflection Rule:
- A point at (r, c) reflects to (c, r) across the main diagonal.
- So, if a square is at (2, 4), its reflection is at (4, 2).

✔ Reflect all shaded squares across the diagonal to complete the other side.

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✔ Grid 4: Diagonal Line (Top-Right to Bottom-Left)

- Line: Diagonal from top-right to bottom-left (like /).
- Given: Shaded squares on one side.
- Task: Reflect across this anti-diagonal.

#### Reflection Rule:
- A point (r, c) reflects to (8 - r, 8 - c) assuming an 8x8 grid.
- Or more simply: reflect over the diagonal that goes from top-right to bottom-left.

✔ For each shaded block, find its mirror across this diagonal and shade it.

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✔ Grid 5: Two Lines – Vertical and Horizontal (Center Cross)

- Lines: Both vertical and horizontal lines through the center → forms a cross.
- This means both reflections must be applied:
- Reflect across vertical line
- Reflect across horizontal line
- Result: The pattern should be symmetric in all four quadrants.

#### Steps:
1. Start with the shaded part (top-left quadrant).
2. Reflect across vertical line → get top-right.
3. Reflect across horizontal line → get bottom-left.
4. Reflect again → get bottom-right.

✔ The full pattern will be symmetric in all directions around the center.

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✔ Grid 6: Two Diagonals (X-shaped)

- Lines: Both diagonals — main diagonal (\) and anti-diagonal (/)
- This means the pattern must be symmetric across both diagonals.

#### Rules:
- Any shaded square must have:
- Its reflection across the main diagonal (r,c) → (c,r)
- Its reflection across the anti-diagonal (r,c) → (8-r, 8-c)
- And also across both combinations.

This creates a very symmetric pattern — often like a star or cross shape.

✔ Shade all required symmetric positions based on existing blocks.

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🧩 Summary of How to Solve Each Grid:

| Grid | Line(s) of Symmetry | How to Complete |
|------|---------------------|------------------|
| 1 | Horizontal | Mirror top to bottom |
| 2 | Vertical | Mirror left to right |
| 3 | Main Diagonal (\) | Swap row and column (r,c) → (c,r) |
| 4 | Anti-Diagonal (/) | Reflect across top-right to bottom-left |
| 5 | Vertical + Horizontal | Mirror across both axes → 4-fold symmetry |
| 6 | Both Diagonals | Mirror across both diagonals → high symmetry |

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✔ Final Answer:

To complete the worksheet:

> For each grid, reflect the shaded blocks across the given line(s) of symmetry. Use the rules of reflection (horizontal, vertical, diagonal) to fill in the missing parts.

Since I can't draw directly here, here’s how you'd do it:

1. Identify the line(s) of symmetry.
2. For each shaded square on one side, locate its mirror image across the line.
3. Shade that mirror square.
4. Repeat until the entire pattern is symmetric.

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💡 Tip: Use a pencil to lightly sketch the reflected points first, then darken them.

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Let me know if you'd like me to describe what the completed patterns look like for any specific grid!