A quadrilateral is a closed shape with exactly four straight sides and four vertices; it can be classified by attributes such as equal side lengths, right angles, and pairs of parallel sides. The classification includes recognizing overlapping categories—for example, a square is both a rectangle and a rhombus—and understanding that a shape’s orientation or size does not change its classification. Formal proofs, diagonal properties, and angle-sum generalizations are beyond this scope.
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Detailed Explanation: Classify quadrilaterals
To classify a quadrilateral, look at its sides and angles.
- Check that the shape is closed.
- Count its straight sides and vertices. It must have exactly 4 of each.
- Look for special attributes:
- Parallelogram: 2 pairs of opposite sides are parallel.
- Rectangle: 4 right angles.
- Rhombus: 4 equal sides.
- Square: 4 equal sides and 4 right angles.
- Kite: 2 pairs of neighboring sides are equal.
A shape can belong to more than one group. Turning or resizing a shape does not change its classification.
Example
Shape has:
- 4 straight sides and 4 vertices
- 4 equal sides
- 4 right angles
- 2 pairs of opposite sides that are parallel
Step 1: Identify the broad group.
It is closed and has exactly 4 straight sides, so it is a quadrilateral.
Step 2: Check the side lengths.
All 4 sides are equal, so it is a rhombus.
Step 3: Check the angles.
All 4 angles are right angles, so it is a rectangle.
Step 4: Check both properties together.
A shape with 4 equal sides and 4 right angles is a square.
So, shape is a:
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Practice:
Quadrilaterals - Is Shape of a Type
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This Worksheet Includes:
- Quadrilaterals - Is Shape of a Type
- Quadrilaterals
- Quadrilaterals (Real World)
- Shapes - 2D Complex
- Polygons - Number of Sides to Name
- Is Shape a Parallelogram (from image)
- Classifying Polygons by Sides
- Quadrilaterals Reversed
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