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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/