Identifying Regular and Irregular Polygons worksheet for students to classify shapes.

Let’s go row by row and fill in the table correctly. We’ll check each shape for:

- Does it have all equal sides?
- Does it NOT have all equal angles? (This means: are some angles different?)
- Is it a regular polygon? (Regular = all sides AND all angles equal)
- Is it an irregular polygon? (Irregular = is a polygon, but sides or angles are not all equal)
- Is it NOT a polygon? (Not a polygon = has curves, or isn’t made of straight lines only)
- What’s its name?

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Row 1: Triangle (looks like a scalene triangle — all sides different)

- Has all equal sides? → No ✗
- Does not have all equal angles? → Yes ✓ (since sides are unequal, angles are too)
- Regular polygon? → No ✗
- Irregular polygon? → Yes ✓ (it’s a triangle with unequal sides/angles)
- Not a polygon? → No ✗ (it IS a polygon — 3 straight sides)
- Name → Scalene triangle

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Row 2: Square

- Has all equal sides? → Yes ✓
- Does not have all equal angles? → No ✗ (all angles are 90°)
- Regular polygon? → Yes ✓ (all sides and angles equal)
- Irregular polygon? → No ✗
- Not a polygon? → No ✗
- Name → Square (or regular quadrilateral)

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Row 3: Parallelogram (slanted rectangle — opposite sides equal, but adjacent sides may differ; angles not 90°)

Assuming it’s a typical non-rectangle parallelogram:

- Has all equal sides? → Probably no ✗ (unless it’s a rhombus — but this looks like a general parallelogram)
Wait — actually, looking at the image, it might be a rhombus? But let’s assume it’s a standard parallelogram where only opposite sides are equal.

Actually, in many worksheets, if it’s drawn as a slanted box without marking sides equal, we assume it’s NOT equilateral.

But to be safe — let’s say:

→ Sides: opposite sides equal, but not all four → so “Has all equal sides?” → No ✗
→ Angles: two acute, two obtuse → so “Does not have all equal angles?” → Yes ✓
→ Regular? → No ✗
→ Irregular polygon? → Yes ✓
→ Not a polygon? → No ✗
→ Name → Parallelogram

BUT — wait! If it were a rhombus (all sides equal), then “has all equal sides” would be yes. But since angles aren’t equal, it wouldn’t be regular.

Looking again — the shape is a parallelogram that’s not a rhombus or rectangle. So:

Final for Row 3:

- Has all equal sides? → No ✗
- Does not have all equal angles? → Yes ✓
- Regular polygon? → No ✗
- Irregular polygon? → Yes ✓
- Not a polygon? → No ✗
- Name → Parallelogram

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Row 4: Heart shape

- Has straight sides? → No — it has curves!
→ So: Not a polygon → Yes ✓
→ Therefore, other columns don’t apply (but we can mark them as N/A or leave blank — but per example, we just check “Not a polygon”)

In the example, they checked “Has all equal sides” and “Does not have all equal angles” even though it’s irregular — but heart is NOT a polygon at all.

So:

- Has all equal sides? → Doesn’t matter — but technically, no, because it’s curved → ✗
- Does not have all equal angles? → Also doesn’t apply → ✗ (or leave blank — but to match format, maybe ✗)
Actually, better to think: since it’s not a polygon, we should ONLY check “Not a polygon”, and leave others unchecked or mark as not applicable.

But in the example, they did check properties even for the star (which is a polygon). For heart, since it’s curved, it’s not a polygon.

So:

- Has all equal sides? → ✗ (not applicable, but we’ll put ✗)
- Does not have all equal angles? → ✗
- Regular polygon? → ✗
- Irregular polygon? → ✗ (because it’s not a polygon at all)
- Not a polygon? → ✓
- Name → Heart (not a polygon)

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Row 5: Right-angled triangle (looks like a right triangle with unequal legs)

- Has all equal sides? → No ✗
- Does not have all equal angles? → Yes ✓ (one 90°, others different)
- Regular polygon? → No ✗
- Irregular polygon? → Yes ✓
- Not a polygon? → No ✗
- Name → Right-angled triangle (or scalene right triangle)

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Row 6: Rectangle (rotated — but still rectangle)

- Has all equal sides? → No ✗ (only opposite sides equal)
- Does not have all equal angles? → No ✗ (all angles 90°)
- Regular polygon? → No ✗ (sides not all equal)
- Irregular polygon? → Yes ✓ (polygon, but not regular)
- Not a polygon? → No ✗
- Name → Rectangle

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Row 7: Pentagon (regular-looking — all sides and angles seem equal)

Assume it’s regular unless shown otherwise.

- Has all equal sides? → Yes ✓
- Does not have all equal angles? → No ✗
- Regular polygon? → Yes ✓
- Irregular polygon? → No ✗
- Not a polygon? → No ✗
- Name → Regular pentagon

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Row 8: L-shape (made of rectangles — 6 sides)

This is a hexagon, but irregular.

- Has all equal sides? → No ✗ (some long, some short)
- Does not have all equal angles? → Actually, all angles are 90° or 270°? Wait — in an L-shape made of squares, internal angles are either 90° or 270° — so NOT all equal → Yes ✓
- Regular polygon? → No ✗
- Irregular polygon? → Yes ✓
- Not a polygon? → No ✗ (it’s made of straight lines, closed shape)
- Name → Irregular hexagon (or L-shaped hexagon)

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Row 9: Plus sign (cross shape — 12 sides?)

Actually, a plus sign made of squares has 12 sides? Let’s count: each arm adds 3 sides, but shared — actually, it’s a dodecagon? Or more simply, it’s a polygon with 12 sides.

But importantly:

- All sides equal? → If drawn symmetrically, yes — each outer edge same length → Yes ✓
- All angles equal? → No — some are 90°, some are 270° → So “Does not have all equal angles?” → Yes ✓
- Regular polygon? → No ✗ (angles not all equal)
- Irregular polygon? → Yes ✓
- Not a polygon? → No ✗
- Name → Cross / irregular dodecagon (but usually called a "plus" shape or Greek cross)

Actually, in geometry, this is often called a “rectilinear polygon” or specifically a “Greek cross”. But for school level, “Plus shape” or “Cross” is fine. And since it has 12 sides, “dodecagon”, but irregular.

But to keep it simple:

Name → Plus shape / irregular dodecagon

But perhaps better: “Irregular 12-gon” or just “Cross”

Looking at example: they said “Star / irregular decagon” — so similar here.

So:

Name → Cross / irregular dodecagon

But let’s confirm side count: a plus sign made of 5 squares (center + 4 arms) has 12 outer edges → yes, 12 sides.

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Now let’s compile the answers row by row.

We’ll write the checks as ✓ or ✗, and names clearly.

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Final Table Answers:

Row 1 (Triangle):
- Has all equal sides: ✗
- Does not have all equal angles: ✓
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Scalene triangle

Row 2 (Square):
- Has all equal sides: ✓
- Does not have all equal angles: ✗
- Regular polygon: ✓
- Irregular polygon: ✗
- Not a polygon: ✗
- Name: Square

Row 3 (Parallelogram):
- Has all equal sides: ✗
- Does not have all equal angles: ✓
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Parallelogram

Row 4 (Heart):
- Has all equal sides: ✗
- Does not have all equal angles: ✗
- Regular polygon: ✗
- Irregular polygon: ✗
- Not a polygon: ✓
- Name: Heart

Row 5 (Right triangle):
- Has all equal sides: ✗
- Does not have all equal angles: ✓
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Right-angled triangle

Row 6 (Rectangle):
- Has all equal sides: ✗
- Does not have all equal angles: ✗
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Rectangle

Row 7 (Pentagon):
- Has all equal sides: ✓
- Does not have all equal angles: ✗
- Regular polygon: ✓
- Irregular polygon: ✗
- Not a polygon: ✗
- Name: Regular pentagon

Row 8 (L-shape):
- Has all equal sides: ✗
- Does not have all equal angles: ✓
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Irregular hexagon

Row 9 (Plus sign):
- Has all equal sides: ✓ (assuming symmetric)
- Does not have all equal angles: ✓
- Regular polygon: ✗
- Irregular polygon: ✓
- Not a polygon: ✗
- Name: Cross / irregular dodecagon

Wait — for the plus sign, do all sides equal? In a standard grid-based plus, yes — each segment is same length. But angles: at the inner corners, you have 270° angles, while outer are 90° — so definitely not all angles equal.

So “Has all equal sides” → ✓
“Does not have all equal angles” → ✓
Then it’s an irregular polygon → ✓

Yes.

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One correction: for Row 3 (parallelogram), if it’s a rhombus, then “has all equal sides” would be ✓. But in the image, it’s drawn as a generic parallelogram — not necessarily rhombus. Since no tick marks, we assume sides not all equal.

Similarly, for Row 7 pentagon — if it’s drawn regularly, we assume regular.

For Row 8 L-shape — it’s clearly irregular.

For Row 9 plus — sides equal, angles not.

Okay, ready to write final answer.

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Final Answer:

Here is the completed table:

| Shape | Has all equal sides | Does not have all equal angles | Regular polygon | Irregular polygon | Not a polygon | Name |
|----------------|---------------------|--------------------------------|-----------------|-------------------|---------------|--------------------------|
| Example (Star) | ✓ | ✓ | | ✓ | | Star / irregular decagon |
| Triangle | ✗ | ✓ | | ✓ | | Scalene triangle |
| Square | ✓ | ✗ | ✓ | | | Square |
| Parallelogram | ✗ | ✓ | | ✓ | | Parallelogram |
| Heart | ✗ | | | | ✓ | Heart |
| Right triangle | ✗ | ✓ | | ✓ | | Right-angled triangle |
| Rectangle | ✗ | ✗ | | ✓ | | Rectangle |
| Pentagon | ✓ | ✗ | ✓ | | | Regular pentagon |
| L-shape | ✗ | ✓ | | ✓ | | Irregular hexagon |
| Plus sign | ✓ | ✓ | | ✓ | | Cross / irregular dodecagon |

Note: For shapes that are regular polygons, we leave "Irregular polygon" blank. For shapes that are not polygons, we only check "Not a polygon" and leave others blank or with ✗ as appropriate. The key is to identify based on properties.