Okay, I may have been slightly inexplicit. A construction is an essential part of a (constructive) proof. Note that nonconstructive proofs really didn’t go over well with ancient geometers, nor with many modern mathematicians.
To pop up the stack, I’m not really confounding construction and proof, as Jinx suggested. In fact, a standard “geometry construction” (the kind of thing the OP was talking about) is a problem asking for a construction with a proof that it is correct.