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ABCD is a quadrilateral in which AB = CD and AD = BC (both pairs of opposite sides equal). Reena argues this forces ABCD to be a parallelogram.
Which justification supports her conclusion?

Class 8Properties of QuadrilateralsGeometry
  • AIf both pairs of opposite sides of a quadrilateral are equal, it is a parallelogram
  • BEqual opposite sides only make it a kite
  • CEqual opposite sides only make it a trapezium
  • DThis is true only if a diagonal is drawn equal to a side

Step-by-Step Solution

A quadrilateral with both pairs of opposite sides equal is a parallelogram (standard converse property, provable via congruent triangles using a diagonal).
Answer: A) If both pairs of opposite sides of a quadrilateral are equal, it is a parallelogram

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