Free Symmetry Worksheet for Grade 3 and 4 - Free Printable

The image is a worksheet titled "Folded Symmetry", designed to help students identify whether a dashed line drawn through a shape represents a line of symmetry or not a line of symmetry. A line of symmetry divides a shape into two mirror-image halves, meaning if you folded the shape along the line, both sides would match perfectly.

Let’s analyze each shape in both columns and explain why it belongs in its respective category.

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✔ Line of Symmetry (Correctly Identified)

1. Triangle (Equilateral)
- The dashed line goes from the top vertex to the midpoint of the base.
- This is a vertical line of symmetry because both halves are mirror images.
- ✔ Correct: It is a line of symmetry.

2. Kite-shaped figure
- The dashed line runs vertically down the center.
- The left and right sides are mirror images.
- ✔ Correct: It is a line of symmetry.

3. Circle
- The dashed line is vertical through the center.
- A circle has infinite lines of symmetry; any line through the center works.
- ✔ Correct: It is a line of symmetry.

4. Star (Regular 5-pointed star)
- The dashed line runs vertically through one point and the opposite valley.
- A regular 5-pointed star has 5 lines of symmetry, and this is one of them.
- ✔ Correct: It is a line of symmetry.

5. Trapezoid (Isosceles Trapezoid)
- The dashed line is vertical and goes through the midpoints of the two parallel bases.
- An isosceles trapezoid has one line of symmetry — this is it.
- ✔ Correct: It is a line of symmetry.

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✘ Not a Line of Symmetry (Incorrectly Placed Line)

1. Pentagon (Regular Pentagon)
- The dashed line is drawn vertically but does not go through a vertex and the midpoint of the opposite side.
- In a regular pentagon, lines of symmetry must pass through a vertex and the midpoint of the opposite side.
- Since this line doesn’t align properly, the two halves won’t match.
- ✘ Correct: Not a line of symmetry.

2. Rectangle
- The dashed line is diagonal.
- A rectangle has two lines of symmetry (vertical and horizontal through the center), but not diagonal.
- Diagonal folding would not result in matching halves.
- ✘ Correct: Not a line of symmetry.

3. Arrow-like hexagon (Chevron shape)
- The dashed line is vertical, but the shape is asymmetrical on the left and right.
- The left side has a sharp inward angle, while the right side is straight.
- Folding along this line wouldn’t produce matching halves.
- ✘ Correct: Not a line of symmetry.

4. Square
- The dashed line is diagonal.
- While a square does have diagonal lines of symmetry, this one is drawn from corner to corner.
- Wait: Actually, a square DOES have diagonal lines of symmetry. So this might be incorrectly placed in the "Not a Line of Symmetry" column.

🔍 Let's clarify:
- A square has 4 lines of symmetry: 2 diagonals, 1 vertical, 1 horizontal.
- If the dashed line is along a diagonal (corner to corner), then it IS a line of symmetry.
- But here, the line appears to be drawn from one corner to the midpoint of the opposite side, which is not a symmetry line.

👉 Looking closely: The dashed line starts at the bottom-left corner and goes to the top-right side, but not to the opposite corner. It's a diagonal cut that doesn't go from corner to corner.

Therefore, this line does not divide the square into two identical halves → Not a line of symmetry.

✔ So the placement is correct.

5. Cross (Plus sign)
- The dashed line is diagonal.
- The cross has symmetry along vertical, horizontal, and both diagonals.
- However, let’s examine: A standard plus-shaped cross (like a Greek cross) has four lines of symmetry: vertical, horizontal, and both diagonals.
- So a diagonal line should be a line of symmetry.

🚨 Wait: The dashed line appears to go from the top-left arm to the bottom-right arm, but doesn’t pass through the center?
- No, actually, in the diagram, it looks like it goes from the top-left corner of the upper arm to the bottom-right corner of the lower arm — passing through the center.

If it passes through the center and the arms are equal, then yes, it is a line of symmetry.

But the worksheet places it under "Not a Line of Symmetry", which is incorrect.

⚠️ Potential Error in Worksheet:
- The cross does have diagonal lines of symmetry.
- So placing it in "Not a Line of Symmetry" is wrong.

✔ Correction: This should be moved to the "Line of Symmetry" column.

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✔ Final Evaluation:

| Shape | Column in Worksheet | Correct? | Explanation |
|-------|---------------------|---------|------------|
| Triangle | Line of Symmetry | ✔ Yes | Vertical line through apex → symmetric |
| Kite | Line of Symmetry | ✔ Yes | Vertical fold → mirror image |
| Circle | Line of Symmetry | ✔ Yes | Any diameter is a line of symmetry |
| Star | Line of Symmetry | ✔ Yes | One of five possible lines |
| Trapezoid | Line of Symmetry | ✔ Yes | Isosceles trapezoid has vertical symmetry |
| Pentagon | Not a Line of Symmetry | ✔ Yes | Line not aligned with symmetry axis |
| Rectangle | Not a Line of Symmetry | ✔ Yes | Diagonal is not a line of symmetry |
| Arrow Hexagon | Not a Line of Symmetry | ✔ Yes | Asymmetrical left/right |
| Square | Not a Line of Symmetry | ✔ Yes | Dashed line is not a diagonal from corner to corner → not symmetric |
| Cross | Not a Line of Symmetry | ✘ No | Error: A diagonal through center is a line of symmetry for a symmetric cross |

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🟩 Conclusion:

- All shapes are correctly classified EXCEPT the cross.
- The cross should be in the "Line of Symmetry" column because a diagonal line through the center does create two matching halves.
- This is likely an error in the worksheet.

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✔ Corrected Answer:

Move the cross from "Not a Line of Symmetry" to "Line of Symmetry".

Otherwise, the rest of the classification is accurate.

Let me know if you'd like a corrected version of the worksheet!