Hint: Lemma 3.3.3 allows you to construct circles such as CD(|AB|). Can you use this to construct edges for your triangle?
If you get stuck, feel free to ask another group for help.
Discussion of Lemma 3.3.4: Wait a second! This is that impossibly complicated and important Axiom 5 that people spent so long trying to prove based on the first four axioms! If it's such a complicated axiom, why are we able to just go ahead and do this using a straightedge and compass?
The reason we can do this is that the surface we are working on is flat -- a white board or piece of paper. We don't have to prove that lines do or do not intersect; we can construct the lines and see whether they do or not. This construction would be impossible on the surface of a sphere.
The text book gives Lemma 3.3.3 as an exercise. How would you go about trying to prove it? Work on this construction in groups of 2 or 3.
We only have three points; what can we do with them?
The first thing we might think of is constructing the lines that join A and B to point C. If we had some way to copy angle BAC so that its vertex was at C, this might complete the proof. Maybe we can copy a triangle to C by copying each of its edge lengths (using our compass?)
Perhaps we decide we want to construct a line perpendicular to line AB, then a line perpendicular to that through C, resulting in a line through C parallel to line AB. We know how to construct perpendicular bisectors of segments (lemma 3.3.2). Can we use that?
We have three distances: |AB|, |BC| and |AC| which we could use to construct circles around the three points: A, B and C. Are any of these circles useful to us?