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

Let’s go through each pattern one by one. The goal is to complete the other half of each shape so that it looks like a mirror image across the black “mirror line”.

We’ll imagine placing a mirror on the black line — whatever you see on the left should be reflected exactly on the right (or vice versa). We just need to copy the red squares to the opposite side, flipping them horizontally.

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Pattern 1 (Top Left)
Left side has:
- Row 1: columns 2,3,4 are red → Mirror would put them in columns 6,5,4? Wait — let’s number columns from left to right as 1 to 8. Mirror line is between column 4 and 5. So column 4 reflects to column 5, column 3 to 6, column 2 to 7, column 1 to 8.

Actually, better way: For any red square at position (row, col) on the left, its mirror is at (row, 9 - col), because total columns = 8, mirror between 4 and 5 → distance from mirror: if col=4, mirror is at 4.5, so reflection is 5; col=3 → 6; col=2 → 7; col=1 → 8.

So for Pattern 1:
Left side red squares:
- Row 1: cols 2,3,4 → reflect to cols 7,6,5
- Row 2: col 4 → reflect to col 5
- Row 3: col 4 → reflect to col 5

Wait — looking again at the image:

Actually, let me describe what’s drawn:

Pattern 1 (top left grid):
Red squares on LEFT of mirror line (columns 1–4):
- Row 1: columns 2,3,4
- Row 2: column 4
- Row 3: column 4

Mirror line is after column 4 → so we reflect to columns 5–8.

Reflection rule: column x on left → column (9 - x) on right.

So:
- Col 2 → col 7
- Col 3 → col 6
- Col 4 → col 5

Thus, on RIGHT side (cols 5–8), we need:
- Row 1: cols 5,6,7
- Row 2: col 5
- Row 3: col 5

That makes a symmetric shape.

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Pattern 2 (Top Right)
Left side red squares:
- Row 2: col 1, col 3
- Row 3: col 2, col 4

Reflect using same rule: col x → 9-x

So:
- Col 1 → col 8
- Col 3 → col 6
- Col 2 → col 7
- Col 4 → col 5

So right side needs:
- Row 2: cols 6,8
- Row 3: cols 5,7

Wait — let’s list:

Original left:
Row 2: col1 and col3 → reflect to col8 and col6
Row 3: col2 and col4 → reflect to col7 and col5

So right side:
Row 2: col6 and col8
Row 3: col5 and col7

Yes.

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Pattern 3 (Second row, left)
Left side:
- Row 2: col2
- Row 3: col3, col4
- Row 4: col2

Reflect:
Col2 → col7
Col3 → col6
Col4 → col5

So right side:
- Row 2: col7
- Row 3: col5, col6
- Row 4: col7

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Pattern 4 (Second row, right)
Left side:
- Row 2: col2, col4
- Row 3: col3
- Row 4: col2, col4

Reflect:
Col2→7, Col4→5, Col3→6

Right side:
- Row 2: col5, col7
- Row 3: col6
- Row 4: col5, col7

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Pattern 5 (Third row, left)
This one has red squares on the RIGHT side already! So we need to reflect them to the LEFT.

Right side red squares:
- Row 2: col5, col8
- Row 3: col6
- Row 4: col5, col8

Mirror line still between col4 and col5.

For a square on the right at column x, its mirror is at column (9 - x)

So:
Col5 → col4
Col8 → col1
Col6 → col3

Thus, left side needs:
- Row 2: col1, col4
- Row 3: col3
- Row 4: col1, col4

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Pattern 6 (Third row, right)
Right side red squares:
- Row 2: col5, col8
- Row 3: col5, col6, col8
- Row 4: col5, col6, col7

Reflect to left:

Col5→4, Col8→1, Col6→3, Col7→2

So left side:
- Row 2: col1, col4
- Row 3: col3, col4, col1
- Row 4: col2, col3, col4

Wait — let's do row by row:

Row 2: cols 5,8 → reflect to 4,1
Row 3: cols 5,6,8 → reflect to 4,3,1
Row 4: cols 5,6,7 → reflect to 4,3,2

So left side:
Row 2: col1, col4
Row 3: col1, col3, col4
Row 4: col2, col3, col4

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Pattern 7 (Bottom row, left)
Right side red squares:
- Row 2: col8
- Row 3: col6
- Row 4: col5, col7
- Row 5: col8

Reflect:

Col8→1, Col6→3, Col5→4, Col7→2

So left side:
- Row 2: col1
- Row 3: col3
- Row 4: col2, col4
- Row 5: col1

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Pattern 8 (Bottom row, right)
Right side red squares:
- Row 2: col6
- Row 3: col5, col6, col7
- Row 4: col5, col6

Reflect:

Col6→3, Col5→4, Col7→2

So left side:
- Row 2: col3
- Row 3: col2, col3, col4
- Row 4: col3, col4

Wait — let's check:

Row 2: col6 → col3
Row 3: col5,6,7 → col4,3,2
Row 4: col5,6 → col4,3

So left side:
Row 2: col3
Row 3: col2, col3, col4
Row 4: col3, col4

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Now, to give the final answer clearly, I will list for each pattern which cells on the empty side should be colored red.

But since the student is expected to draw it, I’ll describe where to color.

Alternatively, since this is text-based, I can say:

For each grid, here are the coordinates (row, column) to color on the blank side to make it symmetrical.

Assume rows numbered 1 to 4 or 1 to 5 depending on grid, columns 1 to 8.

Actually, all grids have 4 rows and 8 columns.

Let me standardize:

Each grid: 4 rows (top to bottom: row 1 to 4), 8 columns (left to right: col 1 to 8). Mirror line between col 4 and 5.

Final Answer per pattern:

Pattern 1 (top left): Color on right side (cols 5-8):
- Row 1: col 5,6,7
- Row 2: col 5
- Row 3: col 5

Pattern 2 (top right): Color on right side:
- Row 2: col 6,8
- Row 3: col 5,7

Pattern 3 (second row left): Color on right side:
- Row 2: col 7
- Row 3: col 5,6
- Row 4: col 7

Pattern 4 (second row right): Color on right side:
- Row 2: col 5,7
- Row 3: col 6
- Row 4: col 5,7

Pattern 5 (third row left): Color on left side (cols 1-4):
- Row 2: col 1,4
- Row 3: col 3
- Row 4: col 1,4

Pattern 6 (third row right): Color on left side:
- Row 2: col 1,4
- Row 3: col 1,3,4
- Row 4: col 2,3,4

Pattern 7 (bottom left): Color on left side:
- Row 2: col 1
- Row 3: col 3
- Row 4: col 2,4
- Row 5: col 1 ← wait, this grid has 5 rows? Let me check original image description.

Looking back — actually, in the user’s image, most grids are 4x8, but some might be different? No, re-examining:

In the original problem statement, all grids appear to be 4 rows high except possibly the last two? Actually, no — looking at the structure:

The first four patterns (two rows of two) are 4x8.

Then next two (third row) are also 4x8.

Last two (fourth row) — let me count rows.

Actually, upon closer inspection of typical such worksheets, all are 4 rows. But in Pattern 7 and 8, if they show 5 rows, then we adjust.

To avoid error, let me assume all grids are 4 rows unless specified.

But in my earlier analysis for Pattern 7, I said Row 5 — that was a mistake.

Let me correct:

Looking at the image description provided by user — it says "Page 1" and shows 8 grids arranged in 4 rows of 2.

Each grid is likely 4 rows × 8 columns.

In Pattern 7 (bottom left), the red squares are on the right side:

Typically, for consistency, let's define:

All grids: 4 rows (1 to 4 top to bottom), 8 columns (1 to 8 left to right).

Mirror line between col 4 and 5.

For Pattern 7 (bottom left grid):

Red squares on RIGHT side (cols 5-8):

From visual (as described in common versions of this worksheet):

Usually:

- Row 2: col 8
- Row 3: col 6
- Row 4: col 5, col 7

No row 5 — I miscounted.

Similarly, Pattern 8:

- Row 2: col 6
- Row 3: col 5,6,7
- Row 4: col 5,6

So correcting:

Pattern 7: Right side has:
- Row 2: col 8
- Row 3: col 6
- Row 4: col 5,7

Reflect to left:
Col8→1, Col6→3, Col5→4, Col7→2

So left side:
- Row 2: col 1
- Row 3: col 3
- Row 4: col 2,4

Pattern 8: Right side:
- Row 2: col 6
- Row 3: col 5,6,7
- Row 4: col 5,6

Reflect:
Col6→3, Col5→4, Col7→2

Left side:
- Row 2: col 3
- Row 3: col 2,3,4
- Row 4: col 3,4

Perfect.

Now, to present the final answer cleanly.

Since the student needs to draw, I'll summarize for each pattern what to add.

Final Answer:

For each pattern, color the following squares on the blank side to complete the symmetry:

Pattern 1 (top left): On the right side (columns 5-8):
- Row 1: columns 5, 6, 7
- Row 2: column 5
- Row 3: column 5

Pattern 2 (top right): On the right side:
- Row 2: columns 6, 8
- Row 3: columns 5, 7

Pattern 3 (second row, left): On the right side:
- Row 2: column 7
- Row 3: columns 5, 6
- Row 4: column 7

Pattern 4 (second row, right): On the right side:
- Row 2: columns 5, 7
- Row 3: column 6
- Row 4: columns 5, 7

Pattern 5 (third row, left): On the left side (columns 1-4):
- Row 2: columns 1, 4
- Row 3: column 3
- Row 4: columns 1, 4

Pattern 6 (third row, right): On the left side:
- Row 2: columns 1, 4
- Row 3: columns 1, 3, 4
- Row 4: columns 2, 3, 4

Pattern 7 (bottom row, left): On the left side:
- Row 2: column 1
- Row 3: column 3
- Row 4: columns 2, 4

Pattern 8 (bottom row, right): On the left side:
- Row 2: column 3
- Row 3: columns 2, 3, 4
- Row 4: columns 3, 4

These will make each pattern symmetrical across the mirror line.