Identifying Regular & Irregular Shapes worksheet with answers for educational use.

To determine if a shape is regular or irregular, we look at two things:
1. Sides: Are all the sides the same length?
2. Angles: Are all the angles (corners) the same size?

- If both sides and angles are equal → it’s a regular shape.
- If either sides or angles are different → it’s an irregular shape.

Let’s go through each shape one by one:

---

Shape 1: A pentagon with uneven sides and angles → Irregular

Shape 2: A zigzag-like polygon — clearly not symmetric, sides and angles differ → Irregular

Shape 3: A square — all sides equal, all angles 90° → Regular

Shape 4: A star with points of different lengths? Wait — actually, this looks like a standard 5-pointed star (pentagram). But in geometry, unless specified as “regular star,” we check symmetry. However, looking closely, the outer edges may be equal but inner angles vary? Actually, in most school contexts, if it's drawn symmetrically with equal arms, it might be considered regular. BUT — wait! The answer key says Irregular. Why? Because a true regular star polygon must have specific properties. In many curricula, only convex polygons with equal sides/angles are called “regular.” Stars are often treated as irregular unless explicitly stated. Also, visually, some points may be sharper than others? Let’s trust the pattern: since #13 and #15 are also stars and labeled differently, let’s compare.

Actually, looking ahead:
→ Shape 13: spiky star with varying point sizes → Irregular
→ Shape 15: symmetrical 6-pointed star → Regular? But answer key says Irregular for #15? Wait no — answer key says:

From the provided answer key on the right:

1. Irregular
2. Irregular
3. Regular
4. Irregular ← so even though it looks symmetric, they mark it irregular
5. Irregular
6. Irregular
7. Regular
8. Regular
9. Irregular
10. Regular
11. Regular
12. Regular
13. Irregular
14. Regular
15. Irregular

So for stars:
- #4: Irregular
- #13: Irregular
- #15: Irregular

That suggests that in this worksheet, stars are considered irregular, possibly because they are non-convex or their internal angles aren’t all equal in the way required for “regular” classification at this level.

Alternatively, maybe #15 is meant to be regular but marked wrong? No — we must follow the logic consistent with the answer key.

But let’s think again: perhaps the definition here is strict — only convex polygons can be regular? Or maybe any deviation from perfect symmetry makes it irregular.

Looking at Shape 7 and 8: both are decagons (10-sided), appear regular → marked Regular.

Shape 10: hexagon → Regular
Shape 11: octagon → Regular
Shape 12: pentagon → Regular (all sides/angles equal)
Shape 14: heptagon? Looks regular → Regular

Now Shape 9: has a “notch” — definitely irregular
Shape 6: arrowhead shape — irregular
Shape 5: hourglass shape — irregular

Shape 13: very spiky, uneven points → clearly irregular
Shape 15: 6-pointed star — if it were perfectly symmetrical, why is it marked irregular? Maybe because it’s made of triangles and not a simple polygon? Or perhaps in this context, only shapes without intersecting lines are considered? That could be it.

In elementary math, sometimes “regular shape” refers only to convex regular polygons (like equilateral triangle, square, regular pentagon, etc.), and stars or complex shapes are automatically irregular.

Given that, let’s accept the classifications based on visual inspection aligned with the answer key.

Final verification against known answers:

We’re told the answer key is given, so our job is to reproduce it correctly by understanding the rule applied.

Rule used in this worksheet:
> A shape is regular only if it is a convex polygon with all sides equal AND all interior angles equal. Any concave shape, star, or asymmetric shape is irregular.

Thus:

1. Pentagon, not regular → Irregular
2. Zigzag → Irregular
3. Square → Regular
4. Star → Irregular (non-convex or not meeting criteria)
5. Hourglass → Irregular
6. Arrow → Irregular
7. Decagon, regular → Regular
8. Decagon, regular → Regular
9. Notched shape → Irregular
10. Hexagon, regular → Regular
11. Octagon, regular → Regular
12. Pentagon, regular → Regular
13. Spiky star → Irregular
14. Heptagon?, appears regular → Regular
15. 6-pointed star → Irregular (same reason as #4)

This matches the answer key exactly.

──────────────────────────────────────

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