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On a straight road, three milestones P, Q and R are placed in order with Q between P and R. The distance PQ = QR. A worker claims that since PQ and QR are each equal to the same length (the gap between consecutive milestones), PQ must equal QR.
Which Euclidean axiom directly supports the worker's claim?

Class 9Euclid's AxiomsGeometry — Foundations
  • AThings equal to the same thing are equal to one another
  • BThe whole is greater than the part
  • CIf equals are added to equals the wholes are equal
  • DAll right angles are equal

Step-by-Step Solution

Both PQ and QR equal the common gap length; by the first axiom, things equal to the same thing are equal, so PQ = QR.
Answer: A) Things equal to the same thing are equal to one another

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