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Which of the following is the MOST efficient single test to prove a quadrilateral is a parallelogram?

Class 9QuadrilateralsGeometry — Quadrilaterals
  • AOne pair of opposite sides is both equal and parallel
  • BOne pair of opposite sides is parallel
  • COne pair of opposite sides is equal
  • DTwo adjacent angles are supplementary

Step-by-Step Solution

If one pair of opposite sides is BOTH equal AND parallel, the quadrilateral is a parallelogram — only one pair needs checking. Just parallel (trapezium) or just equal is insufficient.
Answer: A) One pair of opposite sides is both equal and parallel

Key idea: Tests for a parallelogram

A quadrilateral is a parallelogram if ANY ONE of the following is true:

- Both pairs of opposite sides are parallel (definition).
- Both pairs of opposite sides are equal.
- Both pairs of opposite angles are equal.
- Diagonals bisect each other.
- One pair of opposite sides is **both equal AND parallel**.

That last one is the most efficient — only ONE pair to check, but you need both 'equal' AND 'parallel'.

Don't confuse: just 'one pair parallel' is a trapezium, not a parallelogram.

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