"Let the expert who really understands it, do it. Don't take it in C.H.E.G.G please. I saw it there, i don;t like it"

6-9. Assume that the parallel lines ( and I' have a common perpendicu lar PQ. For any point X on l, let X' be the foot of the perpendicu lar from X to l'. Prove that as X recedes endlessly from P on l, the segment XX' increases indefinitely; see Figure 6.20. (Hint: We saw that it increases in Exercise 4. Drop a perpendicular XY to the lim- iting parallel ray between PX and PX'. Use the crossbar theorem to show that PY intersects XX' in a point Z. Use Proposition 4.5 to show that XZ > XY. Conclude by applying Aristotle's axiom.) P X Z Y Q X' Figure 6.20 Distance between divergently parallel lines increases without bound.Prove Exercise 6.9 In a hyperbolic plane, let & II &' with common perpendicular though P and Q. For any point X on l, let X' be the foot of the perpendicular from X to L'. Prove as X recedes endlessly from P on &, the segment XX' increases indefinitely