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9th Grade Mathematics Example RAFT Role: Audience: Format: Topic: You are a transversal in a 9th grade geometry diagram. The pair of lines that you intersect run parallel to each other. Your audience includes the geometry teacher and his 6th period students. Most of the students are freshmen. You need to write a documentary explaining your existence and your role in the diagram from your geometry book on p. ____. This documentary needs to be written in first person. Your task is to thoroughly explain to Mr. Parsons and the students in the class what a transversal line is and that you have created three sets of congruent angles upon becoming a transversal. W F elcome to my world! I suspect that it’s probably not often that you get to hear from someone as unique as a geometric transversal. I rarely take time for carefree bantering because I am usually frightfully busy keeping the lines I intersect both straight and parallel and the resulting angles congruent. However, I do have a few free moments today to share with you how I came to be. irst of all, I feel like I’d better clear up some disturbing misconceptions that are floating out there about transversals. You may believe, “Once a transversal…always a transversal.” However, that’s not true at all. Every single transversal began life as a simple dot. Some of my less adventurous relatives chose to remain dots. In fact, many of them are still around and spend their time hanging out at the end of sentences or have teemed up with others to become colons or ellipses. Others have moved away from the printed page to become employed as freckles or even age spots on their older clients. It’s a pretty dull life if you ask me. However, not all my ancestors remained simple dots. Many of us wandered away from the nest as soon as we had a chance to broaden our horizons. [We were the more adventurous branch of our family tree! Some of my more flamboyant relatives became wavy lines, segments, and even arcs. In fact, my Uncle Ray hooked up with a buddy to become an obtuse angle. That brings you to me. J ust like my ancestors before me, I started my life as a dot. However, I eventually wandered away to first become a line segment. I eventually graduated to the status of line and finally I was promoted to become a transversal. Now, I’m sure you can sense that I take my job very seriously. In fact, I am quite pleased to say that I am ICC: Characteristics of Effective Instruction in Literacy Resource provided by AEA 267 © 2009 — Permission granted to educational organizations to copy and use http://www.aea267.k12.ia.us/ now fitfully and permanently employed to keep my parallel lines secured and unwavering. You see, I remain permanently connected to them. Because I’ve crossed two parallel lines in my quest for employment, I have created eight very special angles. I f you can picture what I look like it may help as I attempt to clarify my existence. First of all, parallel lines are two lines that never cross. I like to think of my own parallel lines as resembling railroad tracks. In order to prevent a train derailment, those tracks must always be the same distance apart. That’s what parallel means. Now, if a telephone pole fell across those train tracks ~ well, that would be me! A transversal is a special line that crosses a pair of parallel lines and creates eight special angles. The transversal might intersect at 90º~ but does not necessarily need to. In fact, the chance that a transversal crosses the parallel lines at exactly 90º is rather rare [in my opinion.] I elected to bisect my lines at an intentional angle of both 30 and 150 degrees. The eight angles that were formed when I intersected lines a and b are now grouped into three sets. However, before I explain those three groupings, I’d better tell you about some of the specialized terms that involve my role as a transversal. C ongruent or congruency would be an important term related to what I do. To be congruent means to have the same size and same shape. This can be identically sized circles. I like to think of a set of matching dinner plates. They’re all the same size and same shape. Congruency is evident when two rectangles have the same base and height. It is also two equally long line segments or two identical trapezoids. The important term to keep in mind when talking about congruent is identical. Congruency can also relate to measurements. In my job as a transversal I have created four sets of congruent angles. That means that two separate sets of my angles have the same measures. Four of my angles measure 30º. The remaining four angles are 150º. A lternate interior and alternate exterior angles were created when I intentionally landed across those parallel lines. You’ll notice that the word “alternate” means ‘every other.’ That means that neither my interior nor exterior angles directly bump into each other. My alternate interior angles are between my parallel lines but they’re on opposite sides of me. For example, one is on the left side of the transversal and the other alternate interior is on the right side of the transversal. You’ll be able to identify the alternate interior and exterior angles because they are CONGRUENT…[they have the same measure!] A similar story holds for the alternate exterior angles I created in that they are also congruent and on opposite sides of the transversal. [One is on the east, the other is on the west]. I’ve noted them below in the diagram and given them labels so that you can more easily visualize what I’m trying to explain. ICC: Characteristics of Effective Instruction in Literacy Resource provided by AEA 267 © 2009 — Permission granted to educational organizations to copy and use http://www.aea267.k12.ia.us/ This is me, the transversal. 30º 150 º 150 º 30 º You can see the eight angles I created when I stumbled across parallel lines[ ‘a’ and ‘b’]. In the second diagram, I have labeled and named the specific sets of angles. line a 30º 150 º 150 º 30 º line b Corresponding Angles: b, c, f, & g [150 º] a, d, e, & h [30 º] Alternate Interior Angles: d&e [30 º] c&f [150 º] a b c Alternate Exterior Angles: a&h [30 º] b&g [150 º] line a d e f g line b h Anyhow, that’s a little bit about me. Life as a transversal is busy. I hope this explanation has helped you understand the differences between my interior and exterior angles as well as how angles on the left or right sides of me have different labels. Finally, the most important piece to remember [in my mind, at least], is that when a transversal crosses parallel lines, sets of congruent [identical] angles are formed. However, if a transversal crosses lines that are not parallel, the resulting angles are not parallel. Well, that’s all for now. Thanks for listening. ICC: Characteristics of Effective Instruction in Literacy Resource provided by AEA 267 © 2009 — Permission granted to educational organizations to copy and use http://www.aea267.k12.ia.us/