Geometry I: Euclidean Geometry Warmup: Making Quadrilaterals . U We will denote the length of a line segment XY by |XY|. In what follows AB and CD are two given line segments of unequal length, i.e. (AB| # |CD|. 1. Using the definitions, postulates, and the first few propositions in Book I of Euclid's Elements, explain how to construct a quadrilateral PQ RS such that | PQ| = [RS| = [AB| and |PS| = [QR| = [CD|. (5) NOTE. As we'll see later on in the course, such a quadrilateral PQ RS must be a parallel- ogram. 2. Using the definitions, postulates, and the first few propositions propositions in Book I of Euclid's Elements, explain how to construct a rectangle TUVW such that |TU) = [VW| = [AB| and |TW| = JUVI = [CD|. (5) NOTE. You are not being asked to formally prove that your constructions work, but you should include enough detail - especially as what postulates or propositions you're using at each step - to make it easy to check whether the construction actually does work. Later assignments are very likely to ask for actual proofs