Symmetry Worksheets - Free Printable

Let's solve the problem step by step.

Task:

Determine whether each shape has a line of symmetry. If it does, we should indicate "Yes" and draw the line of symmetry. If not, mark "No".

---

A line of symmetry is a line that divides a shape into two identical halves such that one half is the mirror image of the other.

We'll analyze each shape:

---

1. Cylinder (3D shape)

- This is a cylinder, drawn in 2D as a rectangle with curved ends.
- It has vertical symmetry — if you draw a vertical line down the center, both sides are mirror images.
- ✔ Yes – There is a vertical line of symmetry.

> Answer: Yes

---

2. Speech bubble (rectangle with a tail)

- The shape is a rectangle with a triangular "tail" pointing downward.
- The tail breaks the symmetry because it's only on one side.
- No line can divide this shape into two matching halves.
- ✘ No

> Answer: No

---

3. Circle with a flat bottom (like a Pac-Man or rounded pentagon)

- This shape is almost a circle but has a flat edge at the bottom.
- It looks like a circle with a small segment removed at the bottom.
- However, since the bottom is flat and the rest is curved, it might have vertical symmetry if the flat part is centered.
- Assuming the flat edge is symmetrically placed, then yes — a vertical line through the center would reflect both sides.
- ✔ Yes

> Answer: Yes

---

4. Heart

- A classic heart shape has one vertical line of symmetry.
- The left and right sides are mirror images.
- ✔ Yes

> Answer: Yes

---

5. Smiley face (circle with eyes and smile)

- The face has two eyes and a smile.
- If the eyes are symmetric and the smile is centered, then:
- Vertical line through the center divides it into two matching halves.
- But: the eyes are likely not perfectly aligned, and the smile is curved.
- However, assuming they are drawn symmetrically, there is a vertical line of symmetry.
- ✔ Yes

> Answer: Yes

---

6. Rectangle with extensions on both sides (like a cross or plug)

- This shape has a central rectangle with smaller rectangles extending from the top and bottom.
- If the extensions are equal in size and position, it has:
- Vertical symmetry (left-right)
- And possibly horizontal symmetry (top-bottom)
- Since the extensions are on both top and bottom, and if symmetric, a vertical line through the center works.
- ✔ Yes

> Answer: Yes

---

7. Three-quarter circle (missing a quarter)

- This is a circle missing a 90° wedge (a quarter).
- The missing piece is at the top-left, say.
- The shape is asymmetric — no line will make both sides mirror images.
- Even if you try horizontal or vertical lines, the missing piece breaks symmetry.
- ✘ No

> Answer: No

---

8. Lightning bolt

- A zigzag lightning bolt shape.
- It’s jagged and irregular.
- No line can divide it into two mirror-image parts.
- ✘ No

> Answer: No

---

9. Arrow-shaped polygon (chevron)

- This is a right-pointing arrow made of straight lines.
- It has a vertical line of symmetry if it's symmetrical about the center.
- Looking at it: the left and right sides are mirror images.
- ✔ Yes

> Answer: Yes

---

✔ Final Answers:

| Shape | Line of Symmetry? |
|-------|-------------------|
| 1. Cylinder | Yes |
| 2. Speech bubble | No |
| 3. Circle with flat bottom | Yes |
| 4. Heart | Yes |
| 5. Smiley face | Yes |
| 6. Rectangular plug | Yes |
| 7. 3/4 circle | No |
| 8. Lightning bolt | No |
| 9. Arrow | Yes |

---

✏️ How to Show the Lines of Symmetry (if drawing):

For shapes with "Yes", draw a dashed line through the center where the reflection occurs.

- Cylinder: Vertical line through center
- Circle with flat bottom: Vertical line through center
- Heart: Vertical line through the middle
- Smiley face: Vertical line through the center of the face
- Plug shape: Vertical line through the center
- Arrow: Vertical line through the tip and center

---

🟩 Summary:

Yes: 1, 3, 4, 5, 6, 9
No: 2, 7, 8

Let me know if you'd like a visual guide or printable version!