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AP ∥ BQ and O is the mid-point of AB. A line through O meets AP at P and BQ at Q. By which rule is △AOP ≅ △BOQ?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • AASA
  • BSAS
  • CSSS
  • DRHS

Step-by-Step Solution

∠OAP = ∠OBQ (alternate angles, AP ∥ BQ), OA = OB, and ∠AOP = ∠BOQ (vertically opposite). OA is between ∠OAP and ∠AOP: ASA.
Answer: A) ASA

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