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Riya draws two triangles. In the first, two sides are 7 cm and 9 cm with a 40° angle between them. In the second, two sides are 7 cm and 9 cm with the 40° angle NOT between them.
Are the two triangles necessarily congruent?

Class 9Criteria for CongruenceGeometry — Triangles
  • ANo, only the first arrangement (SAS) guarantees a unique triangle
  • BYes, both are SAS
  • CYes, by SSS
  • DNo, neither is determined

Step-by-Step Solution

The included-angle case is SAS (unique). The non-included case is SSA, which is ambiguous, so they need not be congruent.
Answer: A) No, only the first arrangement (SAS) guarantees a unique triangle

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