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In figure, AB = CD and AD = CB. Diagonal BD is common.
Prove which rule shows triangle ABD congruent to triangle CDB, and hence angle A = angle C.

Class 9SSS and RHS CongruenceGeometry — Triangles
  • ASSS, hence angle A = angle C by CPCT
  • BRHS, hence angle A = angle C
  • CAAA, hence sides equal
  • DSAS, hence BD bisected

Step-by-Step Solution

AB=CD, AD=CB, BD=DB (common): SSS gives triangle ABD ≅ triangle CDB; by CPCT angle A = angle C.
Answer: A) SSS, hence angle A = angle C by CPCT

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