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Two surveyors stand at points A and B which are 100 m apart. Each measures the angle to a distant tower T: angle at A = 70°, angle at B = 80°.
A second identical survey gives the same baseline 100 m and the same two angles. Are the two triangles ATB congruent, and why?

Class 9Criteria for CongruenceGeometry — Triangles
  • AYes, by ASA (two angles + included baseline)
  • BNo, angles alone never fix a triangle
  • CYes, by RHS
  • DNo, the baseline is not included

Step-by-Step Solution

The 100 m baseline AB lies between the two measured angles (70° and 80°), so ASA fixes the triangle uniquely.
Answer: A) Yes, by ASA (two angles + included baseline)

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