Shapes and Lines of Symmetry | 4th Grade Geometry Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific shapes in your uploaded image. However, based on the description of the worksheet titled "Shapes and Lines of Symmetry", I can help you solve this type of problem and explain how to approach it.

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🔍 Understanding the Task

The goal is to:
1. Look at each shape.
2. Determine whether a given line (drawn on the shape) is a line of symmetry.
3. Write "yes" if it is a line of symmetry, or "no" if it isn't.

A line of symmetry divides a shape into two mirror-image halves. If you fold the shape along the line, both sides should match perfectly.

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✔ How to Check for Symmetry

For each shape:
- Imagine folding the shape along the drawn line.
- Ask: Do the two halves match exactly?
- If yes → it's a line of symmetry.
- If no → it's not.

Let’s go through common shapes and typical lines:

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📐 Example Analysis (based on typical problems like this):

#### 1. Square with a vertical line through the center
- ✔ Yes – a square has 4 lines of symmetry: vertical, horizontal, and two diagonals.
- A vertical line down the middle will reflect left and right perfectly.

#### 2. Regular Hexagon with a vertical line
- ✔ Yes – regular hexagons have 6 lines of symmetry.
- Vertical line through opposite vertices or midpoints of opposite sides works.

#### 3. Rhombus with a diagonal line
- ✔ Yes – a rhombus has 2 lines of symmetry: along its diagonals.
- So if the line is one of the diagonals → yes.

#### 4. Flower-like shape (e.g., 6-petal flower) with a vertical line
- ✔ Yes – if symmetrically designed, many such shapes have rotational and reflectional symmetry.
- Vertical line may split petals evenly → yes.

#### 5. Diamond (rhombus) with a horizontal line
- ✘ No – unless it's a square, a rhombus does not have horizontal/vertical symmetry unless it's aligned properly.
- But if the line goes through the center horizontally, it may not align the top and bottom — depends on orientation.

Wait: Actually, if the diamond is rotated 45°, then its diagonals are vertical/horizontal. So if the line is along a diagonal, it's a line of symmetry. But if it's horizontal across the middle (not a diagonal), then no.

So check: Is the line a diagonal?

#### 6. Star (e.g., 5-pointed star) with a vertical line
- ✔ Yes – a regular 5-pointed star has 5 lines of symmetry.
- A vertical line through a tip and the midpoint of the opposite side → yes.

#### 7. Key-shaped figure with a vertical line
- ✘ No – keys are usually asymmetric. The "bump" on one side won’t match the other.
- So unless it's perfectly mirrored, likely no.

#### 8. Octagon with a vertical line
- ✔ Yes – regular octagons have 8 lines of symmetry.
- Vertical line through center → yes.

#### 9. Arrow pointing right with a vertical line
- ✘ No – arrows are asymmetric. The tail and tip don’t match across a vertical line.
- But if the line is horizontal through the center? Still no — because the arrowhead is pointed.
- Only if the line were along the axis of the arrow (horizontal) would it be a line of symmetry? Wait: Let's clarify.

Wait: An arrow pointing right:
- If the line is horizontal through the center (top to bottom), does it reflect?
- No — top and bottom aren’t symmetric.
- If the line is vertical down the center (left to right)?
- Then the left side (tail) vs right side (arrowhead) — no, they’re different.
- So no line of symmetry for a standard arrow.

But if the line is along the length (i.e., horizontal line from left to right, but that’s not a line of symmetry).

Actually, an arrow pointing right:
- Usually has no line of symmetry unless it's perfectly symmetric (like a double-headed arrow).
- So likely no.

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✔ Final Answer Format (Example):

| Shape | Line of Symmetry? |
|-------|-------------------|
| Square | Yes |
| Hexagon | Yes |
| Rhombus | Yes (if diagonal) |
| Flower | Yes |
| Diamond | No (if not diagonal) |
| Star | Yes |
| Key | No |
| Octagon | Yes |
| Arrow | No |

> ⚠️ Note: The actual answer depends on how the line is drawn in each case. For example, a rhombus only has symmetry along its diagonals, not horizontal/vertical unless it's a square.

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🧠 Tips:

- Regular polygons (equilateral triangle, square, pentagon, etc.) have multiple lines of symmetry.
- Irregular shapes (like key, arrow) often have none.
- Symmetry requires exact matching — even a small difference means "no".

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If you describe the shapes and the lines (e.g., “a square with a vertical line”, “a star with a line through a point”), I can give you the exact answers!

Would you like to describe each shape and line so I can help fill out the worksheet?