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Riya draws quadrilateral ABCD on graph paper.
She measures and finds AB = CD = 7 cm and AB is parallel to CD.
She wants to claim ABCD is a parallelogram.
Which single theorem justifies her claim directly?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • AA quadrilateral with one pair of opposite sides equal and parallel is a parallelogram
  • BA quadrilateral with equal diagonals is a parallelogram
  • CA quadrilateral with all sides equal is a parallelogram
  • DA quadrilateral with perpendicular diagonals is a parallelogram

Step-by-Step Solution

AB and CD are one pair of opposite sides that are both equal and parallel, which is exactly the stated theorem.
Answer: A) A quadrilateral with one pair of opposite sides equal and parallel is a parallelogram

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