Identify the type of each quadrilateral in this geometry worksheet.

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 four sides are equal (`=`), and all angles are right angles (marked with squares).
- This is a square.

✔ Type: Square

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3)

- One pair of opposite sides appears parallel (top and bottom), but no markings for equal sides or angles.
- Only one pair of parallel sides → trapezoid.

✔ Type: Trapezoid

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4)

- Two pairs of opposite sides are marked as parallel (`||`), and opposite sides are equal (`=`).
- But no right angles.
- This is a parallelogram.

✔ Type: Parallelogram

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5)

- No parallel sides indicated.
- No equal sides.
- No right angles.
- Looks like an irregular quadrilateral.

✔ Type: Irregular Quadrilateral

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6)

- One pair of opposite sides is parallel (`||`), and two adjacent sides are equal (`=`).
- Also, one angle is marked as right angle.
- This is a right trapezoid (a trapezoid with at least one right angle).
- But since only one pair of sides is parallel, it's a trapezoid.

✔ Type: Trapezoid

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7)

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

✔ Type: Square

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8)

- Two pairs of opposite sides are parallel (`||`), and opposite sides are equal (`=`).
- But no right angles.
- This is a parallelogram.

✔ Type: Parallelogram

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9)

- One pair of opposite sides is parallel (`||`), and the other pair is not.
- The non-parallel sides are not equal.
- This is a trapezoid.

✔ Type: Trapezoid

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10)

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

✔ Type: Square

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11)

- Two pairs of opposite sides are parallel (`||`), and opposite sides are equal (`=`).
- But no right angles.
- This is a parallelogram.

✔ Type: Parallelogram

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12)

- One pair of opposite sides is parallel (`||`), and two adjacent sides are equal (`=`).
- Similar to #6, this is a trapezoid with one right angle and adjacent equal sides.
- Still, only one pair of parallel sides.

✔ Type: Trapezoid

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✔ Final Answers:

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

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Notes:

- Squares are also rectangles and rhombuses, but we classify them as squares when all conditions are met.
- Parallelograms include rectangles, rhombuses, and squares — but if not all sides are equal or angles aren't right, it's just a parallelogram.
- Trapezoids have exactly one pair of parallel sides (by definition in many curricula; some define it as *at least* one, but here it's clearly one).

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