Question

it is known that if x + y = 10 then x + y + z = 10 + z. so which of the axioms of euclid's geometry illustrates this?
options=
axiom 1
axiom 2
axiom 3
axiom 4

Answer 1

$$\begin{gathered} \mathrm{It}\mathrm{illustrate}\mathrm{axiom}2\mathrm{of}\mathrm{Euclid}\text{'}\mathrm{s}\mathrm{that}"\mathrm{if}\mathrm{equal}\mathrm{is}\mathrm{added}\mathrm{to}\mathrm{equals},\mathrm{the}\mathrm{wholes}\mathrm{are}\mathrm{equal}". \\ \mathrm{Since}\mathrm{x}+\mathrm{y}=10 \\ \mathrm{We}\mathrm{added}\mathrm{Z}\mathrm{on}\mathrm{both}\mathrm{sides} \\ \Rightarrow \mathrm{x}+\mathrm{y}+\mathrm{z}=10+\mathrm{z} \end{gathered}$$