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ABCD is a parallelogram. On side AB a point E is taken and on side DC a point F is taken such that AE = CF.
Prove-style question: when AECF is formed (vertices A, E, C, F in order), it is a parallelogram because:

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • AAE is equal and parallel to CF
  • BAE = EC
  • CAC is perpendicular to EF
  • Dangle AEC = 90°

Step-by-Step Solution

AE lies on AB and CF lies on DC; AB is parallel to DC, so AE is parallel to CF, and it is given AE = CF. One pair of opposite sides equal and parallel makes AECF a parallelogram.
Answer: A) AE is equal and parallel to CF

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