(1) Let l be a line in absolute geometry, and let H denote a halfplane of l. Let A and B be two distinct points on l. Prove that for any r ∈ R, with r > 0, and for any θ ∈ (0, π), there exists a unique point P in H such that BP = r and m∠ABP = θ.

(2) Let l be a line in absolute geometry. Prove that if P and Q are points on the same side of l, and P and T are points on opposite sides of l, then Q and T are on opposite sides of l.