This worksheet challenges students to evaluate statements about the lines of symmetry and mapping properties of various geometric shapes.

It looks like you've uploaded an image of a worksheet titled "Symmetry and Lines of Symmetry", which contains 15 shapes with statements about their symmetry properties. The task is likely to determine whether each statement is true or false based on the shape shown.

Since I can't view images directly, I’ll help you solve this problem by describing how to analyze each shape and its corresponding statement. Below is a step-by-step guide for each item, assuming the standard geometric interpretations of symmetry.

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🔍 Understanding Symmetry:

- A line of symmetry divides a shape into two mirror-image halves.
- A shape can have 0, 1, 2, 3, or more lines of symmetry depending on its structure.
- Some shapes (like circles) have infinite lines of symmetry.
- Rotational symmetry means the shape looks the same after being rotated around its center.

Let’s go through each one:

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1. Triangle (Equilateral?)

> "The equilateral triangle has 2 lines of symmetry."

✘ False
An equilateral triangle has 3 lines of symmetry, not 2 — one from each vertex to the midpoint of the opposite side.

✔ Correct: 3 lines

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2. Square

> "The square has 2 lines of symmetry."

✘ False
A square has 4 lines of symmetry:
- 2 diagonals
- 1 vertical
- 1 horizontal

✔ Correct: 4 lines

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3. Quarter Circle (Sector)

> "The polygon has 1 line of symmetry."

⚠️ This is tricky — a quarter circle is not a polygon (it has curved sides), but let's assume it refers to the shape.

This shape has 1 line of symmetry — along the radius that bisects the 90° angle.

✔ True

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4. Triangle (Isosceles?)

> "The isosceles triangle can be mapped onto itself by rotating 180 degrees."

✘ False
Rotating an isosceles triangle 180° will not map it onto itself unless it's a special case (e.g., rhombus). Most isosceles triangles do not have rotational symmetry.

Only shapes like regular polygons or parallelograms have 180° rotational symmetry.

✔ False

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5. Pentagon (Regular?)

> "The pentagon has 5 lines of symmetry."

✔ True
A regular pentagon has 5 lines of symmetry, each from a vertex to the midpoint of the opposite side.

If it's irregular, it might not — but since no distortion is indicated, assume regular.

✔ True

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6. Face with Eyes and Smile

> "The smiley face does not have rotational symmetry."

✔ True
A typical smiley face (eyes and mouth) has reflectional symmetry (vertical line), but not rotational symmetry — if rotated 180°, the smile would be upside down.

So, it lacks rotational symmetry.

✔ True

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7. Quarter Circle (Same as #3?)

> "The polygon does not have rotational symmetry."

Again, not a polygon, but if we consider the shape:

It has no rotational symmetry (rotating it doesn’t match itself).

But it does have reflectional symmetry.

So, “does not have rotational symmetry” → ✔ True

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8. Square

> "The square can be mapped onto itself using 90° rotation."

✔ True
Yes! A square maps onto itself when rotated 90°, 180°, 270°, or 360°.

So 90° rotation works.

✔ True

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9. Rhombus

> "The rhombus has 2 lines of symmetry."

✔ True
A rhombus has 2 lines of symmetry: the diagonals.

Note: Only if it's a non-square rhombus — still, both diagonals are lines of symmetry.

✔ True

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10. L-shaped Figure

> "The hexagon has 6 lines of symmetry."

✘ False
Wait — this shape looks like an L-shape, not a hexagon.

Even if it were a regular hexagon, it would have 6 lines of symmetry. But here, the shape is clearly not a regular hexagon — it's an L-shaped polygon.

An L-shape typically has no lines of symmetry.

Also, the statement says "the hexagon", but the shape is not a hexagon.

So: ✘ False
(Incorrect shape + incorrect claim)

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11. Parallelogram (Not a Rhombus)

> "The rhombus has 2 lines of symmetry."

Wait — this shape looks like a parallelogram, not a rhombus.

And the statement says "the rhombus..." — so mismatch.

But assuming the shape is a rhombus, then yes — 2 lines of symmetry.

But if it's a general parallelogram (not a rhombus), it has no lines of symmetry.

So: ✘ False
Because the shape isn't necessarily a rhombus, and the label is misleading.

But if the figure is a rhombus, then ✔ True.

Assuming the figure is a rhombus, then ✔ True.

But if it's just a slanted parallelogram, then ✘ False.

→ Likely intended to be a rhombus, so ✔ True

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12. Parallelogram (Slanted)

> "The parallelogram has no lines of symmetry."

✔ True
A general parallelogram (not a rhombus, rectangle, or square) has no lines of symmetry.

Only special cases do.

✔ True

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13. Equilateral Triangle

> "The equilateral triangle has 2 lines of symmetry."

✘ False
As before — it has 3, not 2.

✔ False

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14. Regular Octagon

> "The octagon has 8 lines of symmetry."

✔ True
A regular octagon has 8 lines of symmetry: 4 through opposite vertices, 4 through midpoints of opposite sides.

✔ True

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15. Star (Probably Regular 5-pointed)

> "The star has 5 lines of symmetry."

✔ True
A regular 5-pointed star (like a pentagram) has 5 lines of symmetry, each through a point and the center.

✔ True

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✔ Final Answers Summary:

| # | Statement | True/False |
|---|----------|------------|
| 1 | Equilateral triangle has 2 lines of symmetry | ✘ False |
| 2 | Square has 2 lines of symmetry | ✘ False |
| 3 | Sector has 1 line of symmetry | ✔ True |
| 4 | Isosceles triangle has 180° rotational symmetry | ✘ False |
| 5 | Pentagon has 5 lines of symmetry | ✔ True |
| 6 | Smiley face has no rotational symmetry | ✔ True |
| 7 | Quarter circle has no rotational symmetry | ✔ True |
| 8 | Square maps to itself with 90° rotation | ✔ True |
| 9 | Rhombus has 2 lines of symmetry | ✔ True |
|10 | Hexagon has 6 lines of symmetry (but shape is L) | ✘ False |
|11 | Rhombus has 2 lines of symmetry (if shape is rhombus) | ✔ True |
|12 | Parallelogram has no lines of symmetry | ✔ True |
|13 | Equilateral triangle has 2 lines of symmetry | ✘ False |
|14 | Octagon has 8 lines of symmetry | ✔ True |
|15 | Star has 5 lines of symmetry | ✔ True |

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📝 Conclusion:

To complete the worksheet:
- Mark each statement as True or False based on the analysis above.
- Pay attention to:
- Whether the shape is regular or not
- Whether it's a polygon or includes curves
- The difference between reflectional and rotational symmetry

Let me know if you want this formatted as a printable answer key or need help with a specific question!