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: It has one pair of parallel sides? Not marked. So no indication.

Thus, it’s just a general quadrilateral.

But usually, such shapes with one pair of parallel sides are trapezoids.

Wait — no markings, so we cannot confirm.

But visually, it might be a trapezoid? But without markings, we can't say.

However, in these types of worksheets, even if not marked, sometimes the shape implies something.

But here, no markings → we must rely on visual cues?

Wait — look at the image again.

Actually, upon closer inspection:
- In #3, the top and bottom sides appear to be parallel (same length, horizontal), but no markings.
- But since no tick marks or parallel lines, we cannot assume.

So unless there’s a marking, we cannot classify it.

But in standard math aids worksheets, they often use visual cues and markings.

Let me recheck: #3 has no markings at all — no equal sides, no right angles, no parallel lines.

So it’s just an irregular quadrilateral.

But actually, it looks like a trapezoid — one pair of parallel sides.

But without markings, we can't be sure.

Wait — the worksheet uses symbols like `||` for parallel, `=` for equal, `⊥` for right angle.

In #3, none of those are present.

So we cannot confirm any special property.

Thus, it’s a general quadrilateral.

But that’s rare.

Alternatively, maybe it’s a trapezoid — but again, no markings.

Wait — let’s look at #5 — similar shape, but also no markings.

Wait — perhaps the shape itself suggests it.

But without markings, we cannot assume.

But in many such worksheets, if the shape is drawn with one pair of sides parallel, it's considered a trapezoid.

But here, no indication.

Wait — perhaps I misread.

Looking back at the image:

- #3: a quadrilateral with two non-parallel sides and two others — appears to have one pair of parallel sides? Maybe.

But no markings.

Wait — compare to #9, which has red dots on the base and top — those are right angles.

Ah! Now I see: some figures have markings, others don’t.

Let’s go one by one carefully.

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Re-analyzing with Markings:

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1)

- Two pairs of opposite sides marked with equal signs (`=`).
- Also, double lines on opposite sides → indicates parallel sides.
- So: opposite sides equal and parallel → parallelogram.
- No right angles.
✔ Type: Parallelogram

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2)

- All four sides marked with `=` → all sides equal.
- All four angles are right angles (small squares).
- So: all sides equal + all angles 90° → square.
✔ Type: Square

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3)

- No markings at all.
- Shape: a quadrilateral with two sides slanted, no obvious symmetry.
- No parallel sides indicated, no equal sides, no right angles.
- So it's an irregular quadrilateral.
✔ Type: Irregular Quadrilateral

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4)

- Opposite sides marked with double lines (`||`) → parallel.
- Also, opposite sides marked with `=` → equal.
- So: opposite sides parallel and equal → parallelogram.
- But note: no right angles, so not a rectangle.
- However, all sides are not equal — only opposite sides are equal.
- So: parallelogram.
✔ Type: Parallelogram

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5)

- No markings.
- Shape: a quadrilateral with one pair of sides possibly parallel? But no indication.
- Visually, it looks like a trapezoid, but no markings.
- So again, no special properties → irregular quadrilateral.
✔ Type: Irregular Quadrilateral

Wait — but compare to #6 and #12 — they have markings.

But #5 has nothing.

So yes — no information → irregular quadrilateral.

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6)

- Two sides marked with `=` (adjacent sides equal).
- One pair of opposite sides marked with `||` → parallel.
- Also, one side has a perpendicular mark (`⊥`) — meaning a right angle.
- So: one pair of parallel sides, a right angle, and two adjacent sides equal.
- This is a right trapezoid with one leg perpendicular to the bases.
- But also, two adjacent sides equal — so it might be a kite-like shape?
- But wait: only one pair of parallel sides → trapezoid.
- And one right angle → right trapezoid.
- But the equal sides are adjacent — so it could be a right trapezoid with equal legs.
- But not a kite because kites have two pairs of adjacent equal sides.
- Here, only one pair of adjacent sides equal.
- So it’s a right trapezoid.
✔ Type: Right Trapezoid

Wait — but the markings:
- Two sides marked with `=` — both adjacent to the same vertex.
- One pair of sides with `||` — indicating parallel.
- And a right angle.

So yes: one pair of parallel sides, one right angle, two adjacent sides equal.

This is a right trapezoid.

✔ Type: Right Trapezoid

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7)

- All sides marked with `=` → all sides equal.
- All angles are right angles (small squares).
- So: all sides equal + all right angles → square.
✔ Type: Square

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8)

- Opposite sides marked with `||` → parallel.
- Also, opposite sides marked with `=` → equal.
- But no right angles.
- So: parallelogram.
- But note: all sides are not equal — only opposite sides are.
- So not a rhombus.
- So: parallelogram.
✔ Type: Parallelogram

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9)

- One pair of opposite sides marked with `||` → parallel.
- Also, the top and bottom have right angles (small red squares).
- So: one pair of parallel sides, and two right angles.
- That means the two non-parallel sides are perpendicular to the bases.
- So it's a right trapezoid.
- But also, the non-parallel sides are equal? No marking.
- Wait — no equal sides marked.
- But the two bases are not equal — one longer than other.
- So: trapezoid with two right angles → right trapezoid.
✔ Type: Right Trapezoid

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10)

- All sides marked with `=` → all sides equal.
- All angles are right angles (small squares).
- So: square.
✔ Type: Square

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11)

- Opposite sides marked with `=` and `||`.
- So: opposite sides equal and parallel.
- No right angles.
- So: parallelogram.
✔ Type: Parallelogram

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12)

- Two adjacent sides marked with `=` (equal).
- One pair of opposite sides marked with `||` → parallel.
- One right angle marked (`⊥`).
- So: one pair of parallel sides, one right angle, two adjacent sides equal.
- Same as #6.
- So: right trapezoid.
✔ Type: Right Trapezoid

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Now let’s summarize:

| # | Type |
|---|------|
| 1 | Parallelogram |
| 2 | Square |
| 3 | Irregular Quadrilateral |
| 4 | Parallelogram |
| 5 | Irregular Quadrilateral |
| 6 | Right Trapezoid |
| 7 | Square |
| 8 | Parallelogram |
| 9 | Right Trapezoid |
| 10 | Square |
| 11 | Parallelogram |
| 12 | Right Trapezoid |

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Final Answers:

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

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Notes:

- Trapezoid: Defined here as having exactly one pair of parallel sides.
- Right Trapezoid: A trapezoid with at least one right angle.
- Parallelogram: Two pairs of parallel sides.
- Square: All sides equal, all angles 90°.
- Irregular Quadrilateral: No special properties.

✔ All answers based on markings and definitions.

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