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In quadrilateral ABCD, AB ∥ DC and AB = DC. Diagonal BD is drawn. By which rule is △ABD ≅ △CDB?

Class 9SAS, ASA and AAS CongruenceGeometry — Triangles
  • ASAS
  • BSSS
  • CASA
  • DAAS

Step-by-Step Solution

AB = CD (given), ∠ABD = ∠CDB (alternate angles, AB ∥ DC) and BD is common. The angle lies between AB and BD (and between CD and DB), so SAS. It follows that AD = CB, so ABCD is a parallelogram.
Answer: A) SAS

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