square / Rectangle / Rhombus / Parallelogram / - Fill and Sign ... - Free Printable

Problem:

The task is to classify the given quadrilaterals into one of the following categories: square, rectangle, rhombus, parallelogram, or trapezoid. The image shows 9 quadrilaterals labeled as 1 through 9.

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Solution:

To solve this problem, we need to analyze each quadrilateral based on its properties. Here are the definitions of each type of quadrilateral:

1. Square: A quadrilateral with all sides equal and all angles equal to 90°.
2. Rectangle: A quadrilateral with opposite sides equal and all angles equal to 90°.
3. Rhombus: A quadrilateral with all sides equal but not necessarily right angles.
4. Parallelogram: A quadrilateral with opposite sides parallel and equal.
5. Trapezoid: A quadrilateral with at least one pair of parallel sides.

Now, let's classify each quadrilateral step by step:

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#### Quadrilateral 1:
- Shape: A quadrilateral with two pairs of parallel sides.
- Properties: Opposite sides are equal in length.
- Classification: Parallelogram

#### Quadrilateral 2:
- Shape: A quadrilateral with one pair of parallel sides.
- Properties: The non-parallel sides are not equal.
- Classification: Trapezoid

#### Quadrilateral 3:
- Shape: A quadrilateral with two pairs of parallel sides.
- Properties: All sides are equal in length.
- Classification: Rhombus

#### Quadrilateral 4:
- Shape: A quadrilateral with all sides equal and all angles equal to 90°.
- Properties: All sides are equal, and all angles are right angles.
- Classification: Square

#### Quadrilateral 5:
- Shape: A quadrilateral with opposite sides equal and all angles equal to 90°.
- Properties: Opposite sides are equal, and all angles are right angles.
- Classification: Rectangle

#### Quadrilateral 6:
- Shape: A quadrilateral with one pair of parallel sides.
- Properties: The non-parallel sides are not equal.
- Classification: Trapezoid

#### Quadrilateral 7:
- Shape: A quadrilateral with opposite sides equal and parallel.
- Properties: Opposite sides are equal and parallel.
- Classification: Parallelogram

#### Quadrilateral 8:
- Shape: A quadrilateral with all sides equal and all angles equal to 90°.
- Properties: All sides are equal, and all angles are right angles.
- Classification: Square

#### Quadrilateral 9:
- Shape: A quadrilateral with one pair of parallel sides.
- Properties: The non-parallel sides are not equal.
- Classification: Trapezoid

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Final Answer:

\[
\boxed{
\begin{array}{ccc}
1. \text{Parallelogram} & 2. \text{Trapezoid} & 3. \text{Rhombus} \\
4. \text{Square} & 5. \text{Rectangle} & 6. \text{Trapezoid} \\
7. \text{Parallelogram} & 8. \text{Square} & 9. \text{Trapezoid}
\end{array}
}
\]