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A student writes a proof: 'AC = BC (given). D is the midpoint of AB so AD = DB. Therefore by an axiom, AC + AD = BC + DB.'
Which axiom justifies the final step?

Class 9Euclid's AxiomsGeometry — Foundations
  • AIf equals are added to equals, the wholes are equal
  • BThe whole is greater than the part
  • CThings which coincide are equal
  • DHalves of equals are equal

Step-by-Step Solution

AC = BC and AD = DB are two pairs of equals. Adding the respective equals gives AC + AD = BC + DB (adding equals to equals).
Answer: A) If equals are added to equals, the wholes are equal

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