> ?A>M bjbj== "(WWl2hjjjjjj$K k
EhhP0:0]"]Prior to beginning this activity, students need to be familiar with how Cabri Jr. "! operates. Start the Cabri Jr. "! application with a new sketch. Open the menu and then select the Line tool to draw a line near the bottom of the screen.Open the menu and then select the Point tool, option Point, to place a point above and to the right of the left hand control point of the line.Open the +" menu and then select the Parallel tool to construct the line parallel to the first line drawn, passing through the point just placed in the drawing.Open the menu and then select the Point tool, option Point on, to place a point on the parallel line fairly close and to the right of the point placed in second step.Open the menu and then select the Hide/Show tool, option Object, to hide the lines in the drawing. Then open the menu and then select the Quad. tool to connect the four points (in either a clockwise or counterclockwise order) to form a quadrilateral. Have the students discuss if this quadrilateral is special in any way. They should be able to see that it is a trapezoid and explain why it is that kind of quadrilateral.Open the menu and then select the Measure tool, option D. & Length, to measure the lengths of the left and right edges of the trapezoid. You may need to remind the students that they will have to wait for a short time in order to measure a single edge of a trapezoid and not the trapezoids perimeter. After getting the length of an edge, depress the + key to get a second decimal place in the lengths value. Move those lengths to convenient places on the screen.Use the a key to select the upper right hand point of the trapezoid. Use it to move left and right, noting the lengths of the edges as you do so. As you carry out this investigation, you will find a place at which the trapezoid becomes a triangle. To the left of that place the figure ceases being a quadrilateral. After you move the point to the right, there is a place at which the two displayed lengths become equal (or very close to it). Pose the question What special kind of trapezoid is this? If they are not visibly equal, they will change from the left edge being less than the right edge to the right edge being less than the left edge. The question to pose in that case is What is the situation somewhere in between those two points?After you move the point to the right, there is another place at which the two displayed lengths become equal (or very close to it). Pose the question What special kind of trapezoid is this? If they are not visibly equal, they will change from the height being greater than the base to the height being less than the base. The question to pose in that situation is What is the case somewhere in between those two points?
If you want to avoid this discussion, you can keep the number of decimal places in the lengths to be one. In that way, it is quite likely that, to one decimal place, the edge lengths will be equal. In my experience, however, it is healthy to talk about the situations that often arise with two decimal place accuracy.
After the work on the calculator, you can pose the questions At what point did the two measured edges first become congruent? Did any of the trapezoids fundamental properties change, i.e., number of edges, straightness of its edges, etc.? Do you think an isosceles trapezoid is a special case of a trapezoid?
After considering the first situation, you can pose the questions At what other point did the two measured edges become congruent? Did any of the trapezoids fundamental properties change, i.e., number of edges, straightness of its edges, etc.? Do you think a parallelogram is a special case of a trapezoid?
With teachers, the first question will draw little discussion. The second question could be quite a different story. Many teachers learned a geometry in which a trapezoid was defined as a quadrilateral with exactly one set of parallel edges. Under that definition, a trapezoid could never be a parallelogram. Students, on the other hand, have little difficulty with this kind of development. This is especially true if they have the experience of seeing why an equilateral triangle is a special case of isosceles triangle and a square is a special case of rectangle.
On a personal note, I was one of those teachers who learned the restrictive definition of trapezoid. It was work with dynamic geometry that convinced me that defining a trapezoid as a quadrilateral with at least one set of parallel edges makes more sense.
*<>hrz&0:V`$&PZjRTXjl
&
2
^_ij]^_`ab jU jU jxU jU5OJQJ\ j"U j U jU jU jU5\OJQJ^J_HH^J_HHIRVX ^`a\TdE$$If0X'`4
a$d$Ifa$ $$Ifa$\]cd\]
̼XVE$$If0"X'*64
a$
!x$If^a$$x$Ifa$
!x$If2$$IfX'`'4
a
j1U
M$a$$xa$ 1h/ =!8"8#8$%Dd0
#A"}$6OU9YD@=Q$6OU9iyx1J`/štEtn(^Kbg?1j(F)I*It]b1;>=(vQ(ޏVf$O)ݤ4OWf:?3Q{1fe Tt].@t].]чtm=kL..wa}.Ѕ봠t].@tt].@tvsWC~JBO]t.t].@tt].@t].@.@t].@tt].@zm](8tttttuZ]]u]~V'@`Xiډ.Ѕ.}u.t@ڸ
.@ttttttg3ԙiu|P4Dd0
#A"t`꽖`3XsPE@=H`꽖`3Xsiyx1NQ@PHpt.
h,]lMhkqqb yIƌ"|KDܦA~h|QrVG<S7ݘt$fﵘt&i
%D1˧*t].@tx~Xźޗk./0~QG]xt].@t].@].@t].@Z.@t].@tt].@t]]|s](3t>.t.a=z}zou`tta?.tata}.Ѕ:;].@t].@kUfZ]`e.t.t.t.t.t].@}]Ūtt.t.N.t.t.t].@]6tay?4;LDd0
#A"
m9Pqm=@=e
m9Pqiy3x=Np᷁Edn&z74@%tٳX!RɓQBɿ壈t]b1:>=(b2+[Oc;v繽7+~[nY4}Q?k-rOngY>eY].@t].@Ebyz_1m<^tatѼ(t.\].@t].@Ѕ.@ЅqǏբ]]]mz\@@M.Ѕ.ЅB@^C@tt].@t].@@=BomߦǓ. (p~ӂ.@t].@@t].@t]l{.Ѕ.C@@@@iu.tMMtqnt.t봿utt]KZqtvk^t.tA7ϻWFBNy]]8F@VƘ3Hj~Dd0
#A":6Qtl(ZNlR @=d:6Qtl(ZNiy2x1N`ᯁEdn&z74@%tٳX6|ɓ`B&IC18q;bxQ嬈A]]DB-]]sZBBBBBx_.`]c>(;gڨDd0
#A"$y]y(<&4f@=y]y(<&4iyx?J3AwI
E
+Ih'!<P,=FkbG\u
Du3|Owg恉-"<}in(Ex{2Ʃ$=8^Gq,xH]NREycLT>0c\J*BBBBBBBBBBBb+
ap!.w
c.#?Q>B\5B휗8B\!7\yq}ˇg.!B9/q!.Ȯu̇up^.z'd͓ur^\ҺOgͧcr&2sx:>U:0c4c].@t].@ﻢ
.E][a@Q^Qr]ӅҦABlgc]}\o]`tVK֧]Xh]B:]/]Խ}.tܧmgx.\]uXe6uKЅ.r?s.ׅ.tQe{_҅.t>Q5g]BwyT?c|^w]B߯aubSE ],;Em]"߷拏zЅ.t]>yK/}]ta:]_҅yBi0O |Յ.~I].[~ ]8E>]]=ﺇ}.t]G5]t]8t].@t]].@t].@Bt].@t]8t].i]s%7b`Dd0
#A"
s}#cX2I@=
s}#cX2Iiyx=NAoƂPrLvh,=\Khg1"0,,3ɛ`uݝVq)u3e/m?rvQݰN|^Tp6Lmz>],ϳ,k.@t].@ź+_t.bӿ۲u_(]K^u.ttnv>]]]ԹoaBЅ.7BЅ>GЅ.Ѕ.tAy.t]|]Bu]bmZΛх.vQeZj]袸.>Uc{/jt]9ov^'汶9G]so.E}]t~V]~#tta]B袈]~vQ}ĠhwEC@畵.tA;:.Ѕ.hr?]Ьy$jЅ.w0s횣]]乎kAK?]KBt].@t].].@t].@tt].@t].].@(˲~Q2^<>X<~ڄDd0
#A "
XiW0w@=
XiW0wiyx?N*A
"ڙ!<XzFkbcDE/;;I> /'ԯ/ӓ*nGUt&@/x9pԍN{?k<%7Y2L7éVHL=0c<].@t].@^ǿ
.XnØׁ..G>Jr}]]]4s~ ABBԇr:@@@yWz0o]B@@ί.p~utЅ.\Ǣ-YwMBEq}g]ջ]tӇp=]>[9tuO>BЅ.Ͼn:Oi~Ѕybu_֫mΓn~[dۼuaϻ'R/.tG~^@х.tQoT'Ѕ.tAٽ<]]P\@̿jt/tt].@tt].@t].].@t].@t].@hja?y|0y܀\Dd0
#A
"s }+L8u@=s }+L8iyzx=N`Edn&z74@%tٳ)$Sߴ|eq?\/|}1xݏDdq;bf
yi0q.Ͳ?ok,&WM{t{%St`t>QBta]]]t{:.Ѕ.Ѕ.E?֛>c]]]}Є5]]]tOb@ۘuSvu8]/E*u.tW]69㸠@t].@t]t].@t].@t].@t].].@c%wP
i8@8NormalCJ_HaJmH sH tH <A@<Default Paragraph Font()+,^`a\]cd\ ]
M
000000000000000000000000000000000 \
mqejd,K333,KCb
BillCC:\Professional\Calculator Workshops\Special Cases of Trapezoid.doc)+,^`a\]cd\ ] @
4@
@UnknownGz Times New Roman5Symbol3&z Arial;TT1E9Eo00? TI84EmuKeys"1hfܨ~F $8890d;d2qHXPPrior to beginning this activity, students need to be familiar with how Cabri Jr
Bill Kring
Bill KringOh+'0 ,< P\
x
QPrior to beginning this activity, students need to be familiar with how Cabri JrerioBill KringgillillNormaliBill Kringg15lMicrosoft Word 9.0t@t@/E(@L0՜.+,0<hp
ESD 112; QPrior to beginning this activity, students need to be familiar with how Cabri JrTitle
!"#$%'()*+,-/012345789:;<=@Root Entry F 0BData
!1Table&WordDocument"(SummaryInformation(.DocumentSummaryInformation86CompObjjObjectPool 0 0
FMicrosoft Word Document
MSWordDocWord.Document.89q