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A trapezium is a quadrilateral with at least one pair of parallel sides. Using this definition, is every parallelogram also a trapezium?

Class 8Understanding QuadrilateralsQuadrilaterals
  • ANo, because a parallelogram has two pairs of parallel sides
  • BYes, because a parallelogram has at least one pair of parallel sides
  • CYes, because every quadrilateral is a trapezium
  • DNo, because a parallelogram has no parallel sides

Step-by-Step Solution

A parallelogram has two pairs of parallel sides, so it certainly has at least one pair. By the definition, every parallelogram is a (special) trapezium.
Answer: B) Yes, because a parallelogram has at least one pair of parallel sides

Key idea: The quadrilateral family tree

Order from most general to most special:

```
Quadrilateral
├── Trapezium (one pair of parallel sides)
├── Kite (two pairs of adjacent equal sides)
└── Parallelogram (two pairs of parallel sides)
├── Rectangle (4 right angles)
│ └── Square (4 right angles + all sides equal)
└── Rhombus (4 equal sides)
└── Square (also)
```

A square is BOTH a rectangle and a rhombus — it's the most special kind of parallelogram. A rectangle and a rhombus are both parallelograms. Trapeziums and kites are quadrilaterals but not parallelograms.

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