Grade 4 Geometry Worksheet: Classifying Quadrilaterals

Let's solve the problem step by step.

Task:

Classify each of the 9 quadrilaterals shown in the worksheet as one of the following:
- Square
- Rectangle
- Rhombus
- Parallelogram
- Trapezoid

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Definitions to Remember:

1. Square:
- All four sides are equal.
- All four angles are 90°.
- A special type of rectangle and rhombus.

2. Rectangle:
- Opposite sides are equal and parallel.
- All angles are 90°.
- Not all sides need to be equal (unless it's a square).

3. Rhombus:
- All four sides are equal.
- Opposite sides are parallel.
- Opposite angles are equal.
- Angles are not necessarily 90°.

4. Parallelogram:
- Opposite sides are equal and parallel.
- Opposite angles are equal.
- Not all sides or angles are necessarily equal.

5. Trapezoid:
- Exactly one pair of opposite sides is parallel.
- The other two sides are not parallel.

> Note: In some regions, "trapezoid" is defined as having *at least* one pair of parallel sides. But in this context (Grade 4), it's typically the exclusive definition: exactly one pair of parallel sides.

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Now let’s analyze each figure:

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1.

- Looks like a slanted parallelogram.
- Opposite sides are parallel and equal.
- Sides are not at right angles.
- All sides appear equal? No — only opposite sides look equal.
- So: Parallelogram
✔ Answer: Parallelogram

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2.

- One pair of opposite sides is parallel (top and bottom).
- The other two sides are not parallel.
- It has a trapezoidal shape.
- This is a trapezoid.
✔ Answer: Trapezoid

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3.

- Looks like a slanted rhombus.
- All four sides appear equal.
- Opposite sides are parallel.
- Angles are not 90°.
- So: Rhombus
✔ Answer: Rhombus

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4.

- Four right angles.
- Opposite sides are equal and parallel.
- But adjacent sides are different lengths.
- So: Rectangle (not a square)
✔ Answer: Rectangle

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5.

- All sides appear equal.
- All angles are 90°.
- So: Square
✔ Answer: Square

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6.

- One pair of opposite sides is parallel (top and bottom).
- The other two sides are not parallel.
- This is a trapezoid.
✔ Answer: Trapezoid

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7.

- Four right angles.
- Opposite sides are equal and parallel.
- Adjacent sides are different lengths.
- So: Rectangle
✔ Answer: Rectangle

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8.

- All sides appear equal.
- All angles are 90°.
- So: Square
✔ Answer: Square

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9.

- One pair of opposite sides is parallel (top and bottom).
- The other two sides are not parallel.
- This is a trapezoid.
✔ Answer: Trapezoid

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✔ Final Answers:

| Number | Shape |
|--------|----------------|
| 1 | Parallelogram |
| 2 | Trapezoid |
| 3 | Rhombus |
| 4 | Rectangle |
| 5 | Square |
| 6 | Trapezoid |
| 7 | Rectangle |
| 8 | Square |
| 9 | Trapezoid |

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Summary of Classifications:

- Squares: 5, 8
- Rectangles: 4, 7
- Rhombuses: 3
- Parallelograms: 1
- Trapezoids: 2, 6, 9

Note: Some shapes can belong to multiple categories (e.g., squares are also rectangles and rhombuses), but here we classify based on the most specific name that fits.

Let me know if you'd like a visual explanation or printable version!