1. The problem statement, all variables and given/known data If ABCD and AFED are Lambert quadrilaterals (see Fig. 3.6.16), prove, in neutral geometry, that if C, D, and E are collinear, then the geometry is Euclidean. 2. Relevant equations I have provided a picture of the shape in question. 3. The attempt at a solution Here are the theorems I think that are important to this proof: By Thm 3.6.7 (just the number given in the book), the 4th angle of a Lambert quadrilateral (∠EDA and ∠CDA) is either right or acute angle. By Thm 3.6.8 we know that the measure of the side included between 2 right angles is less than or equal to the measure of the opposite side. By Thm 4.4.5 If, under a correspondence, the three interior angles of one triangle are congruent to the corresponding interior angles of a second triangle, then the triangles are similar. What I did was make ABCD into 2 triangles and AFED into 2 triangles. For a ABCD, a diagonal line from E to A. And for AFED, a diagonal line from C to A. Doing this we can see by AAA Similarity Condition for Triangles, the triangles are congruent to each other. Thus, making C, D, and E collinear. Am I on the right track? Or have the right idea?