4. Again, assume that MM' is the common perpendicular segment be- tween I and l'. Let A and B be any points of l such that M * A * B and drop perpendiculars AA' and BB' to l'. Prove that AA' AC. In words: The greater side is opposite the greater summit angle (Figure 4.16). PROOF: Assume first BD > AC. Then by definition there is a unique point E between B and D such that AC = BE. Then JABEC is Saccheri,SACCHERI AND LAMBERT QUADRILATERALS 179 E A B Figure 4.16 so by the previous proposition, ACE = BEC. E is interior to ACD (use Exercise 28). It then follows from the exterior angle the- orem and Proposition 3.21 that XD AC (RAA conclusion)