Identifying Regular & Irregular Shapes Worksheet Download - Free Printable

Let's solve the problem step by step.

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Objective:

Determine whether each shape is regular or irregular.

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Definitions:

- A regular shape has:
- All sides of equal length.
- All interior angles equal.
- It is both equilateral and equiangular.

- An irregular shape has:
- Sides of different lengths and/or angles of different measures.

Note: The shapes shown are polygons (closed figures with straight sides). We will assess based on symmetry, side lengths, and angles.

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Now, let’s analyze each shape:

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1) Trapezoid (quadrilateral)
- Two parallel sides, but other sides not equal.
- Not all sides or angles equal.
→ Irregular

2) Wavy-shaped polygon (zigzag)
- Has uneven sides and angles; clearly not symmetrical.
→ Irregular

3) Square
- Four equal sides, four right angles.
→ Regular

4) Star (5-pointed star)
- This is a regular star polygon (like a regular pentagram).
- All points and sides are symmetric and equal.
→ Regular

5) Hourglass-like shape (two triangles joined at apex)
- Symmetrical, but sides are not all equal (top and bottom segments differ in length).
- Angles also vary.
→ Irregular

6) Arrowhead-like shape (with one point)
- Asymmetric; sides and angles vary.
→ Irregular

7) Octagon (8-sided)
- Looks like a regular octagon — all sides and angles appear equal.
→ Regular

8) Octagon (8-sided)
- Similar to #7, appears symmetrical with equal sides and angles.
→ Regular

9) Pentagon with one "bump"
- One side is longer or angled differently.
- Not symmetrical.
→ Irregular

10) Hexagon (6-sided)
- Appears symmetrical with equal sides and angles.
→ Regular

11) Octagon (8-sided)
- Looks like a regular octagon.
→ Regular

12) Pentagon (5-sided)
- Sides and angles do not appear equal.
- Irregular pentagon.
→ Irregular

13) Complex star (spiky, many points)
- Though it looks symmetric, the number of points and proportions suggest it might be a regular star polygon.
- If all spikes are identical and evenly spaced, it’s regular.
- This appears to be a regular 10-pointed star (or similar), symmetric.
→ Regular

14) Heptagon (7-sided)
- Appears symmetrical with equal sides and angles.
→ Regular

15) Star (6-pointed)
- This is a regular hexagram (like a Star of David), made from two overlapping equilateral triangles.
- All sides and angles are equal.
→ Regular

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✔ Final Answers:

| Number | Shape Type |
|--------|----------------|
| 1 | Irregular |
| 2 | Irregular |
| 3 | Regular |
| 4 | Regular |
| 5 | Irregular |
| 6 | Irregular |
| 7 | Regular |
| 8 | Regular |
| 9 | Irregular |
| 10 | Regular |
| 11 | Regular |
| 12 | Irregular |
| 13 | Regular |
| 14 | Regular |
| 15 | Regular |

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📝 Answer Key (for the blank lines):

1. Irregular
2. Irregular
3. Regular
4. Regular
5. Irregular
6. Irregular
7. Regular
8. Regular
9. Irregular
10. Regular
11. Regular
12. Irregular
13. Regular
14. Regular
15. Regular

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✔ Summary:
Regular shapes: 3, 4, 7, 8, 10, 11, 13, 14, 15 → 9 regular shapes
Irregular shapes: 1, 2, 5, 6, 9, 12 → 6 irregular shapes

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