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In the figure, AC = BD (two segments along a line).
If BC is the common middle part, a student concludes AB = CD by subtracting BC from both equal lengths.
Which axiom is used?

Class 9Euclid's PostulatesGeometry — Foundations
  • AIf equals are added to equals
  • BIf equals are subtracted from equals, the remainders are equal
  • CThe whole is greater than the part
  • DAll right angles are equal

Step-by-Step Solution

AC = AB + BC and BD = BC + CD. Since AC = BD and BC is common, subtracting BC from each gives AB = CD.
Answer: B) If equals are subtracted from equals, the remainders are equal

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