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ABCD is a parallelogram. P and Q are points on diagonal BD such that DP = BQ.
To prove APCQ is a parallelogram, the key step is to show that:

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • AThe diagonals of APCQ bisect each other
  • BAP = AQ
  • CAC is perpendicular to PQ
  • Dangle PAQ = 90°

Step-by-Step Solution

Diagonals AC and BD of parallelogram ABCD bisect each other at O. With DP = BQ, O is also the midpoint of PQ, so diagonals AC and PQ of APCQ bisect each other, proving it is a parallelogram.
Answer: A) The diagonals of APCQ bisect each other

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