This problem was taken from Joseph Gallian's "Contemporary Abstract Algebra", 8th edition.
Chapter 23, Exercise 1, Page 402: If $a$ and $b$ are constructible numbers and $a ≥ b > 0$, give a geometric proof that $a + b$ and $a - b$ are constructible.
Honestly, I'm not able to actually start on this problem because the textbook does not provide many examples of geometric proofs. Also, the definition of a "constructible number" does not come with much to go on. In the textbook (page 400) it says:
To begin, we call a real number $\alpha$ constructible if, by means of an unmarked straightedge, a compass, and a line segment of length $1$, we can construct a line segment of length $|\alpha|$ in a finite number of steps.
I suspect the answer to this is actually really trivial, I just haven't seen an axiomatic treatment of any "geometric proof" in this text, so I'm lost on where to start.