Geometry Worksheets | Polygons Worksheets - Free Printable

Let's solve the problem step by step. The task is to identify the type of each quadrilateral based on its properties (such as parallel sides, equal sides, right angles, etc.).

We’ll go through each figure one by one and determine the correct classification.

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Definitions Recap:

- Parallelogram: Two pairs of opposite sides are parallel.
- Rectangle: A parallelogram with four right angles.
- Square: A rectangle with all sides equal (so it has 4 right angles and 4 equal sides).
- Rhombus: A parallelogram with all sides equal (but not necessarily right angles).
- Trapezoid: Exactly one pair of parallel sides.
- Kite: Two pairs of adjacent sides are equal.
- Irregular Quadrilateral: No special properties (no parallel sides, no equal sides, no right angles).

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Now let’s analyze each shape:

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1)

- Opposite sides are marked as equal (`=`, `=`), and there are two pairs of parallel sides (indicated by the double lines).
- But no right angles shown.
- This is a parallelogram.

✔ Type: Parallelogram

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2)

- All sides are equal (`=` marks), and all angles are right angles (square corners).
- This is a square.

✔ Type: Square

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3)

- Only one pair of sides appears to be parallel? Wait — actually, no markings for parallel sides or equal sides.
- It looks like an irregular trapezoid, but no parallel sides indicated.
- Actually, only one side seems to have a slight slant, and no markings suggest anything.
- But wait — check carefully: No parallel sides, no equal sides, no right angles.
- So it's just a general quadrilateral.

But looking at the shape: it has one pair of parallel sides? Not clear from markings.

Wait — no markings at all except the shape. Let’s assume no symbols mean no special properties.

So this is an irregular quadrilateral.

But wait — in standard problems like this, if there are no markings, we can’t assume anything.

But look again — this shape has no parallel sides, no equal sides, no right angles → so it's just a trapezoid?

Wait — actually, only one pair of sides may be parallel? But no indication.

In many such worksheets, if no markings are present, it’s assumed to be a trapezoid if it looks like one.

But here, the top and bottom are not parallel? The angle suggests otherwise.

Actually, upon closer inspection, this shape has no parallel sides → then it’s just an irregular quadrilateral.

But more likely, since it looks like a trapezoid, and no other info, perhaps it's a trapezoid.

Wait — in #9, there is a trapezoid with one pair of parallel sides marked with red lines.

So in #3, no markings → probably irregular quadrilateral.

But let’s see what others show.

Wait — maybe I’m missing something.

Let’s re-express: Markings matter.

Look at #3: no parallel lines marked, no equal sides, no right angles → so it's just a general quadrilateral.

But typically, if it’s a trapezoid, they mark the parallel sides.

So #3: No markings → Irregular quadrilateral

But let’s compare to #5 — same thing.

Wait — actually, #5 also has no markings.

But #3 and #5 both look like trapezoids?

Wait — #3 has a slanted top and bottom, but not parallel.

Actually, #3 has no parallel sides → irregular quadrilateral

But let’s look at #6 — it has two sides marked as equal (`=`), and one pair of parallel sides (double lines). That’s a kite?

Wait — kite has two pairs of adjacent equal sides.

Let’s go one by one.

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1)

- Opposite sides equal and parallel (marked with `=` and parallel lines)
- No right angles
- → Parallelogram

✔ Parallelogram

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2)

- All sides equal (`=`), all angles right angles (squares)
- → Square

✔ Square

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3)

- No markings at all
- Looks like a random quadrilateral
- No parallel sides, no equal sides, no right angles
- → Irregular Quadrilateral

✔ Irregular Quadrilateral

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4)

- Opposite sides are parallel (double lines), and opposite sides are equal (`=`)
- But no right angles
- This is a parallelogram (same as #1)

✔ Parallelogram

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5)

- No markings
- Looks like a trapezoid? But no parallel sides marked
- Again, no indicators
- → Irregular Quadrilateral

Wait — but it might have one pair of parallel sides? But no marking

So unless marked, we can't assume.

→ Irregular Quadrilateral

✔ Irregular Quadrilateral

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6)

- One pair of sides marked as equal (`=`), and another pair marked as equal (`=`), but adjacent sides
- Also, one pair of sides has parallel lines (double lines)
- So: One pair of parallel sides, and two pairs of adjacent equal sides
- That fits a kite? But kite doesn’t require parallel sides.

Wait — kite: two pairs of adjacent equal sides.

Here: left side and right side are marked equal (`=`), and the top and bottom are marked equal? Wait — no.

Wait — the markings:
- Top and bottom: `=` signs → meaning those sides are equal?
- Left and right: `=` signs? Wait — no, only one `=` on the left and one on the right.

Wait — actually:
- The left and right sides are marked with `=` — so those are equal?
- And the top and bottom have `=` — so those are equal?

But that would make it a parallelogram? But also, one pair of parallel sides marked with double lines.

Wait — double lines on the top and bottom → so top and bottom are parallel

And equal sides marked on left and right and top and bottom?

Wait — actually, look closely:

- The top and bottom have `=` signs — so those sides are equal
- The left and right have `=` signs — so those are equal
- Also, top and bottom have parallel lines (double lines) → so they are parallel

So: one pair of parallel sides, and opposite sides equal → that’s a rectangle? But no right angles.

Wait — but no right angles shown.

So: one pair of parallel sides, opposite sides equal → but that’s not enough.

Wait — actually, if both pairs of opposite sides are equal, and one pair is parallel, then the other must be too — making it a parallelogram.

But here, only top and bottom are marked as parallel.

But top = bottom, and left = right — and top || bottom

Then left and right must also be parallel? Not necessarily.

But in Euclidean geometry, if a quadrilateral has one pair of opposite sides equal and parallel, then it’s a parallelogram.

Yes! That’s a theorem.

So: top and bottom are equal and parallel → so it's a parallelogram

But then left and right should also be parallel.

But the diagram shows only one pair of parallel lines.

Wait — maybe the left and right are not parallel?

But the markings: top and bottom have double lines → parallel

Left and right have single lines → not marked as parallel

But top and bottom are equal and parallel → so the figure is a parallelogram

So left and right must also be parallel.

But the diagram doesn’t show that.

Wait — perhaps the double lines are only on top and bottom → so only one pair parallel.

But if top and bottom are equal and parallel, then the figure is a parallelogram.

So even if not marked, it must be.

But in this case, the top and bottom are marked with `=` and `||` → so equal and parallel

Then it must be a parallelogram

But also, left and right are marked with `=` → so they are equal

So it's a parallelogram with equal adjacent sides? No — left and right are opposite sides.

Wait — left and right are opposite sides.

So: Opposite sides equal and one pair parallel → implies parallelogram

So yes → Parallelogram

But wait — if opposite sides are equal and one pair is parallel, then it's a parallelogram

So #6 is a parallelogram

But wait — is it a rhombus? Only if all sides equal.

Here, top = bottom, left = right, but no indication that top = left.

So not necessarily a rhombus.

So → Parallelogram

But let’s confirm the markings:

- Top and bottom: `=` and `||` → equal and parallel
- Left and right: `=` → equal
- So: two pairs of equal opposite sides, and one pair of parallel sides → but if one pair of opposite sides is equal and parallel, then it’s a parallelogram

Yes → Parallelogram

✔ Parallelogram

But wait — this is confusing because #6 looks like a kite?

Wait — no, because top and bottom are marked as equal and parallel, so it’s a parallelogram

So answer: Parallelogram

But let’s move on and come back.

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7)

- All sides marked equal (`=`), and all angles are right angles (squares)
- → Square

✔ Square

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8)

- Opposite sides are marked with `=` and `||` → so parallel and equal
- But no right angles
- So → Parallelogram

✔ Parallelogram

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9)

- One pair of sides marked with `||` → so parallel
- And non-parallel sides are not marked equal
- But top and bottom are not equal (no `=`), but parallel
- So exactly one pair of parallel sides → Trapezoid

✔ Trapezoid

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10)

- All sides equal (`=`), and all angles are right angles (squares)
- → Square

✔ Square

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11)

- Opposite sides are equal (`=`), and parallel (`||`)
- But no right angles
- So → Parallelogram

✔ Parallelogram

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12)

- Two pairs of adjacent sides marked equal (`=`):
- Top and left: `=`
- Right and bottom: `=`
- And one pair of sides marked as parallel (top and bottom have `||`)
- So: Two pairs of adjacent equal sides, and one pair of parallel sides
- This is a kite? But kites don’t have parallel sides usually.

But kite: two pairs of adjacent sides equal.

Here: top = left, and right = bottom → so adjacent sides equal

Also, top and bottom are parallel → so it's a kite with one pair of parallel sides

But that’s possible.

But also, if a kite has one pair of parallel sides, it could be a rhombus? No — rhombus has all sides equal.

Here, top = left, but top ≠ right (unless marked)

Wait — top = left, right = bottom, but top ≠ right (no marking)

So not all sides equal.

So it’s a kite

But kites do not necessarily have parallel sides.

But this one does.

So it’s a kite with one pair of parallel sides

But is it a trapezoid? Yes — because it has one pair of parallel sides.

But the question is: what is the most specific name?

It has two pairs of adjacent equal sides → kite

And one pair of parallel sides → trapezoid

But kite is more specific than trapezoid?

Not necessarily — some kites are trapezoids.

But in this case, since it has two pairs of adjacent equal sides, it’s a kite

So → Kite

But wait — look at #6 again — it was ambiguous.

Let’s clarify #6:

Revisit #6:

- Top and bottom: `=` and `||` → equal and parallel
- Left and right: `=` → equal
- So: top = bottom, left = right, top || bottom
- Since one pair of opposite sides is equal and parallel, it’s a parallelogram
- Then left and right must also be parallel
- So it’s a parallelogram
- But not necessarily a rhombus (unless all sides equal)

But top = bottom, left = right, but no sign that top = left → so not a rhombus

So → Parallelogram

✔ Parallelogram

Now #12:
- Top = left (adjacent)
- Right = bottom (adjacent)
- Top and bottom are parallel (`||`)
- So: kite (two pairs of adjacent equal sides)
- And one pair of parallel sides → so it's also a trapezoid
- But kite is the more specific term if we know the side equality

So → Kite

But wait — kites are defined by two pairs of adjacent equal sides, which this has.

So yes → Kite

✔ Kite

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Now let’s summarize:

| # | Shape | Type |
|---|-------|------|
| 1 | Opposite sides equal and parallel, no right angles | Parallelogram |
| 2 | All sides equal, all right angles | Square |
| 3 | No markings, irregular | Irregular Quadrilateral |
| 4 | Opposite sides equal and parallel, no right angles | Parallelogram |
| 5 | No markings, irregular | Irregular Quadrilateral |
| 6 | One pair of opposite sides equal and parallel, other opposite sides equal | Parallelogram |
| 7 | All sides equal, all right angles | Square |
| 8 | Opposite sides equal and parallel, no right angles | Parallelogram |
| 9 | One pair of parallel sides (marked), non-parallel sides not equal | Trapezoid |
| 10 | All sides equal, all right angles | Square |
| 11 | Opposite sides equal and parallel, no right angles | Parallelogram |
| 12 | Two pairs of adjacent sides equal, one pair of parallel sides | Kite |

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Final Answers:

1) Parallelogram
2) Square
3) Irregular Quadrilateral
4) Parallelogram
5) Irregular Quadrilateral
6) Parallelogram
7) Square
8) Parallelogram
9) Trapezoid
10) Square
11) Parallelogram
12) Kite

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✔ Final Answer:

```
1) Parallelogram
2) Square
3) Irregular Quadrilateral
4) Parallelogram
5) Irregular Quadrilateral
6) Parallelogram
7) Square
8) Parallelogram
9) Trapezoid
10) Square
11) Parallelogram
12) Kite
```

Let me know if you'd like a printed version or explanation per shape!