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ABCD is a parallelogram and AP, CQ are perpendiculars from A and C to diagonal BD (P and Q on BD).
To prove AP = CQ, one shows triangle APB congruent to triangle CQD. Which rule applies?

Class 9Conditions for a ParallelogramGeometry — Quadrilaterals
  • AAAS
  • BSSS
  • CSAS with included angle 90
  • DRHS only

Step-by-Step Solution

In triangles APB and CQD: angle APB = angle CQD = 90°, angle ABP = angle CDQ (alternate angles, AB parallel CD), and AB = CD (opposite sides). By AAS the triangles are congruent, so AP = CQ.
Answer: A) AAS

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