Symmetry Worksheets - Free Printable

It looks like you've uploaded an image of a worksheet with the learning objective (L.O.):

"To identify reflective symmetry in patterns."

The task involves analyzing several grid-based patterns and determining whether they have reflective symmetry, specifically vertical reflective symmetry, as indicated by the blue double-headed arrows pointing up and down — suggesting a vertical line of symmetry.

Let’s go through each pattern one by one and analyze whether it has reflective symmetry across the vertical line shown (i.e., if one side is a mirror image of the other).

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🔍 Step-by-Step Analysis

We’ll examine each of the 6 grids (3 rows, 2 columns), checking for vertical reflective symmetry.

> ✔ Reflective symmetry means: If you fold the shape along the vertical line, both sides match perfectly.

---

#### 🟦 Top Left Pattern
```
Grid: 10x4
Red squares at:
- Row 1: Col 2, 4, 5
- Row 2: Col 3
- Row 3: Col 1
```

Blue square at:
- Row 2: Col 5

Now check symmetry across the central vertical line (between column 5 and 6). Let's compare left and right sides.

- Column 1 ↔ Column 9
- Column 2 ↔ Column 8
- Column 3 ↔ Column 7
- Column 4 ↔ Column 6
- Column 5 ↔ Column 5 (middle)

But there are no squares on the right side (columns 6–10) that mirror the left.

For example:
- Red at (1,2) → should mirror to (1,8), but no red there.
- Red at (1,4) → mirror at (1,6)? No red.
- Blue at (2,5) → middle, so okay, but only if symmetric.

However, left side has more colored squares than right. Right side has nothing.

✘ No reflective symmetry

---

#### 🟥 Top Right Pattern
```
Red squares:
- Row 1: Col 3, 4
- Row 2: Col 3, 4
- Row 3: Col 3, 4
```

This forms a 3×2 block centered at columns 3–4.

Check reflection over the vertical line between col 4 and 5?

Wait — the blue arrow goes from top to bottom, but where is the line of symmetry?

Assuming the line is between column 5 and 6, since the arrow is centered.

But the red block is from col 3–4, which is on the left.

So:
- Col 3 ↔ Col 7
- Col 4 ↔ Col 6
- But the red squares are only on the left, not mirrored on the right.

So:
- (1,3) → should mirror to (1,7): no red
- (1,4) → (1,6): no red

✘ No reflective symmetry

---

#### 🟦 Middle Left Pattern
```
Red and blue squares:
- Row 1: Col 2, 3, 4 (red)
- Row 2: Col 2, 3, 4 (blue)
- Row 3: Col 2, 3, 4 (red)
```

Wait, let's look carefully:

Actually:
- Row 1: Col 2 (red), Col 3 (red), Col 4 (blue)
- Row 2: Col 2 (blue), Col 3 (red), Col 4 (red)
- Row 3: Col 2 (red), Col 3 (blue), Col 4 (red)

Wait — this seems messy.

Wait, better to count:

From the image:
- The shape is a 3x3 block from columns 2–4, rows 1–3.
- It's filled with colors: red and blue in a checkerboard-like pattern.

But does it reflect across the center?

Let’s suppose the line of symmetry is between column 4 and 5.

Then:
- Left side: cols 1–4
- Right side: cols 5–10

But all colored squares are in cols 2–4, and no colored squares on the right side.

So unless the pattern is symmetric within itself, we need to see if it's symmetric across a vertical axis inside the pattern.

But the arrow is drawn vertically, implying the axis of symmetry is somewhere in the middle of the grid, likely between col 5 and 6.

Since all colored blocks are on the left side (cols 2–4), and nothing on the right, it cannot be symmetric.

✘ No reflective symmetry

---

#### 🟩 Middle Right Pattern
```
Colored squares:
- Row 1: Col 4 (blue), Col 5 (green)
- Row 2: Col 4 (green), Col 5 (red)
- Row 3: Col 4 (red), Col 5 (blue)
```

This is a 3x2 block from col 4–5, row 1–3.

Again, all colored squares are on the left side (cols 4–5), and nothing on the right (cols 6–10).

So unless the pattern is symmetric across col 4.5, i.e., between col 4 and 5, we need to check.

But the blue arrow is centered, suggesting the axis is around column 5 or 6.

If the axis is between col 5 and 6, then:

- Col 4 ↔ Col 6
- Col 5 ↔ Col 5 (but col 5 is on the left side)

But the pattern is only in cols 4 and 5, and not mirrored to the right.

So:
- (1,4) → should have a matching square at (1,6)? No.
- (1,5) → (1,5) is on the axis? But only if it's central.

But even if the axis is between col 4 and 5, the pattern is not symmetric because:
- (1,4)=blue, (1,5)=green → not equal
- (2,4)=green, (2,5)=red → different
- (3,4)=red, (3,5)=blue → different

So not symmetric across col 4.5 either.

✘ No reflective symmetry

---

#### 🟨 Bottom Left Pattern
```
Red square at (1,2)
Blue square at (1,3)
```

Only two squares, both in row 1, cols 2 and 3.

Nothing else.

Is this symmetric across a vertical line?

Suppose axis is between col 2 and 3 → then:
- (1,2) ↔ (1,3): red vs blue → different

Not symmetric.

If axis is between col 3 and 4 → then:
- (1,2) ↔ (1,4): (1,2)=red, (1,4)=empty → no

✘ No reflective symmetry

---

#### 🟩 Bottom Right Pattern
```
Blue at (1,2)
Red at (1,3)
Green at (1,4)
Blue at (2,2)
Red at (2,3)
Green at (2,4)
```

So a 2x3 block: cols 2–4, rows 1–2.

Colors:
- Col 2: blue, blue
- Col 3: red, red
- Col 4: green, green

So same color in each column.

Now, is this symmetric across a vertical line?

Let’s suppose the axis is between col 3 and 4.

Then:
- Col 2 ↔ Col 4
- Col 3 ↔ Col 3 (center)

Compare:
- (1,2)=blue ↔ (1,4)=green → not same
- (2,2)=blue ↔ (2,4)=green → not same

So not symmetric.

What if axis is between col 2 and 3?

Then:
- Col 2 ↔ Col 3
- (1,2)=blue ↔ (1,3)=red → different

No.

Or between col 4 and 5? Then:
- Col 2 ↔ Col 6 → no squares

✘ No reflective symmetry

---

✘ Final Conclusion:

After analyzing all six patterns, none of them appear to have reflective symmetry across the vertical line shown.

But wait — perhaps I misread the position of the symmetry line.

Let me re-express the idea:

In many such worksheets, the blue arrow indicates the potential line of symmetry, and students are to determine whether the pattern is symmetric about that line.

But in all cases, the colored shapes are on the left side, and nothing on the right, so unless the pattern is symmetric within its own area, it fails.

But here’s a possibility: maybe the axis is not at the center of the grid, but rather within the pattern?

Wait — look again at the top-right pattern:

It has a 3x2 red block from col 3–4, row 1–3.

But if the axis is between col 3 and 4, then:

- Col 3 ↔ Col 4
- So (1,3) ↔ (1,4): both red → good
- (2,3) ↔ (2,4): both red → good
- (3,3) ↔ (3,4): both red → good

✔ So yes! This pattern is symmetric across the line between col 3 and 4.

But the blue arrow is drawn from top to bottom, centered in the grid, not necessarily aligned with the pattern.

Ah! Here’s the key: the blue arrow is indicating the potential line of symmetry, but it may not be correct.

So the task is to determine if the pattern has reflective symmetry, and if so, draw the line of symmetry — or mark it.

But in this worksheet, the arrow is already drawn, so we must check if that line is actually a line of symmetry.

So let's assume the blue arrow represents a candidate line of symmetry — and we must decide whether the pattern is symmetric with respect to that line.

Let’s now assume the line of symmetry is the vertical line between column 5 and 6 (since the arrow is placed there).

Then, for a pattern to be symmetric, every colored square on the left (col ≤ 5) must have a mirror image on the right (col ≥ 6).

Let’s check each pattern again under this assumption.

---

🔁 Re-analysis: Symmetry Across Line Between Col 5 and 6

#### 1. Top Left:
- Colored squares:
- (1,2), (1,4), (1,5)
- (2,3), (2,5)
- (3,1)

Mirror positions:
- (1,2) → (1,8) → no
- (1,4) → (1,6) → no
- (1,5) → (1,5) → on axis? But (1,5) is blue, and no other square at (1,5) — but mirror would be itself only if axis is at 5.5

But (1,5) is on the left side of the line (between 5 and 6), so mirror is (1,6) — but no square.

✘ Not symmetric

#### 2. Top Right:
- (1,3), (1,4), (2,3), (2,4), (3,3), (3,4) — all in cols 3–4
- Mirror: (1,8), (1,7), etc. → none
✘ Not symmetric

#### 3. Middle Left:
- All in cols 2–4 → mirror would be cols 8–10 → no squares
✘ Not symmetric

#### 4. Middle Right:
- (1,4), (1,5), (2,4), (2,5), (3,4), (3,5) — cols 4–5
- Mirror: (1,6), (1,7), etc. → no
✘ Not symmetric

#### 5. Bottom Left:
- (1,2), (1,3) → mirror: (1,8), (1,7) → no
✘ Not symmetric

#### 6. Bottom Right:
- (1,2), (1,3), (1,4), (2,2), (2,3), (2,4)
- Mirror: (1,8), (1,7), (1,6), (2,8), etc. → no
✘ Not symmetric

---

🚫 So, NONE of the patterns are symmetric across the indicated line (between col 5 and 6).

But wait — perhaps the line of symmetry is not between 5 and 6, but within the pattern?

Maybe the arrow is meant to show where the student should draw the line, not that it’s already correct.

But the instruction says: "identify reflective symmetry in patterns", and the arrow is already drawn.

Alternatively, maybe some patterns are symmetric, but we’re missing something.

Let’s look at top-left pattern again:

- (1,2), (1,4), (1,5), (2,3), (2,5), (3,1)

Wait — (1,5) and (2,5) are both on the same column, and the arrow is at col 5–6.

But (1,5) = blue, (2,5) = blue — but no corresponding squares on the right.

Still not symmetric.

Wait — what if we consider horizontal symmetry? But the arrow is vertical, so it’s about vertical reflection.

Another idea: maybe the pattern is symmetric across a vertical line that is not the one shown, and the student is to determine if any symmetry exists.

But the task is to identify reflective symmetry, and the arrow might be a hint.

But based on the current layout, none of the patterns have reflective symmetry across the vertical line shown.

However, let’s look at the top-right pattern: a 3x2 red block from col 3–4.

If the line of symmetry were between col 3 and 4, then yes — it would be symmetric.

But the arrow is drawn in the center of the grid, not at col 3.5.

So unless the student is supposed to ignore the arrow and find their own line, or mark it correctly, we can't say.

But the way it's presented, the arrow is fixed, so likely the task is to check if the pattern is symmetric across that line.

Given that, none are symmetric.

But that seems odd — probably one is.

Let’s try bottom-right pattern:

- (1,2)=blue, (1,3)=red, (1,4)=green
- (2,2)=blue, (2,3)=red, (2,4)=green

So it's a striped pattern.

If we reflect across a line between col 3 and 4, then:
- (1,2) ↔ (1,4): blue ↔ green → not same
- (1,3) ↔ (1,3): red → stays → ok
- (2,2) ↔ (2,4): blue ↔ green → not same

No.

Wait — what if the pattern is symmetric across a horizontal line? But the arrow is vertical.

Perhaps the student is to draw the line of symmetry if it exists, but here the arrow is already there.

Alternatively, maybe the correct answer is that none have symmetry, but that’s unlikely.

Let’s look for a pattern that is symmetric.

Try top-left again:

- (1,2), (1,4), (1,5), (2,3), (2,5), (3,1)

Can we find a line where left mirrors right?

Suppose line at col 4.5:

- (1,2) ↔ (1,7) → no
- (1,4) ↔ (1,5) → (1,4)=red, (1,5)=blue → not same
- (2,3) ↔ (2,6) → no
- (3,1) ↔ (3,8) → no

No.

Wait — perhaps the intended answer is that the top-right pattern is symmetric across the line between col 3 and 4, but the arrow is misplaced.

But in that case, the student should draw the correct line.

Given the ambiguity, and since the arrow is drawn in the center, and no pattern has symmetry across the center, the likely conclusion is:

> ✔ None of the patterns have reflective symmetry across the indicated vertical line.

But that seems harsh.

Wait — let’s look at the bottom-left pattern:

- (1,2)=red, (1,3)=blue

If the line is between col 2 and 3, then:
- (1,2) ↔ (1,3): red ↔ blue → not same

No.

Unless the pattern is symmetric across a line through col 2.5, but still not.

I think the most likely scenario is that none of the patterns are symmetric across the given line, so the answer is:

> ✘ None of the patterns exhibit reflective symmetry across the indicated vertical line.

But let’s double-check the top-right pattern:

- Three rows, two columns of red squares: cols 3–4, rows 1–3

This is a rectangle.

A rectangle has vertical symmetry if it's centered on the axis.

But here, it's from col 3–4, so if the axis is at col 3.5, then yes — it is symmetric.

So if the line of symmetry is between col 3 and 4, then yes.

But in the worksheet, the arrow is drawn at the center of the grid, which is between col 5 and 6.

So unless the student is to draw a new line, or accept that the arrow is wrong, we can't say.

Perhaps the intended task is to recognize that the top-right pattern has vertical symmetry, and the arrow is just a guide.

But the arrow is in the wrong place.

Given the confusion, I think the best answer is:

> 🟩 The top-right pattern has reflective symmetry across the vertical line between columns 3 and 4.
> However, the arrow shown is not at that position, so the pattern is not symmetric across the indicated line.

Similarly, other patterns do not have symmetry.

So final answer:

> ✔ Only the top-right pattern has reflective symmetry, but not across the indicated line.

But since the task is to identify reflective symmetry in patterns, and the arrow is just a visual aid, perhaps the student is to mark the correct line.

But based on the image as provided, none of the patterns are symmetric across the given line.

Therefore, the solution is:

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✔ Final Answer:

After examining all six patterns:

- None of the patterns are symmetric across the vertical line shown (between columns 5 and 6).
- The top-right pattern has reflective symmetry across a vertical line between columns 3 and 4, but this is not the line indicated.
- Therefore, no pattern exhibits reflective symmetry across the given line.

📝 Explanation:

Reflective symmetry means that one side of the pattern is a mirror image of the other when folded along the line of symmetry. For a pattern to be symmetric across the indicated line (between columns 5 and 6), every colored square on the left must have a matching square on the right at the same row and mirrored column. In all cases, the colored squares are only on the left side, with no corresponding squares on the right, so no reflective symmetry exists across the given line.

Students should learn to verify whether the indicated line is truly a line of symmetry by comparing each cell.

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Let me know if you'd like me to provide a corrected version or suggest how to teach this concept.