Pentagon diagonal - parallel ratio proof 1. The problem statement, all variables and given/known data Suppose P is a convex pentagon such that each diagonal is parallel to one side. Prove that the ratio of the length of a diagonal to that of its corresponding side is the same for all ﬁve diagonals, and compute this ratio 2. Relevant equations 3. The attempt at a solution I think they mean a pentagon where each vertices is connected by an edge. So there is a pentagon in the middle surrounded by obtuse and acute triangles. So if you label the sides of the original pentagon each side is say a+b, with the bases of the acute triangles are say b and the sides are say a. Then the ratio of the paralleled sides is a+b:2a+b? Not really sure how i am meant to prove this though?