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AD and BC are equal perpendiculars to segment AB, on opposite sides, and CD meets AB at O. By which rule is △AOD ≅ △BOC?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • AASA with the right angles only
  • BAAS
  • CSAS
  • DSSS

Step-by-Step Solution

∠OAD = ∠OBC = 90°, ∠AOD = ∠BOC (vertically opposite), and AD = BC (opposite ∠AOD and ∠BOC respectively, not between the angles): AAS. Then OA = OB, so CD bisects AB.
Answer: B) AAS

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