1. Let AB  and CD  be two parallel lines and let EF  be a line intersecting them at points G and H, respectively. Three types of angle relationships follow.
2. First, alternate angles (such as ∠AGH and ∠GHD) are equal. (This is the converse of Book 1 Proposition 27.)
3. Second, any exterior angle and its corresponding interior angle (such as ∠EGB and ∠GHD) are equal. (This is the converse of Book 1 Proposition 28a.)
4. Third, any two interior angles on the same side of EF  (such as ∠BGH and ∠GHD) add up to two right angles. (This is the converse of Book 1 Proposition 28b.)
5. This is the first proposition in Euclid's Elements that depends on Postulate 5 for its proof.