```Date: Oct 8, 1992 5:31 PM
Author: Tom McDougal
Subject: similarity -- cool approach

Though I am a newcomer to this group, I hope you won't mind my sharing thefollwing technique for introducing triangle similarity, which I got fromJohn Benson of Evanston Twp. H.S.:On an overhead transparency, draw a triangle whose sides are integerlengths, say 3cm, 4cm, 5cm.Carefully position the overhead projector so that the projected image hasinteger lengths, say 30 in., 40 in., 50 in.Place a clear ruler alongside one of the sides of the triangle on theoverhead.  Ask the class, "How long is that side?"Inevitably some kid will say, "3 cm."  Smile, then point to the projectedimage:  "*THAT* is 3 cm?"  Measure the (projected) side, repeat for othersides, build a table of the findings (kids will predict the last side):side  triangle  image 1       3 cm    30 in 2       4 cm    40 in 3       5 cm    50 inThen John moves the projector a little bit so that the projected sides areno longer such nice multiples of the original, and goes through the processagain.  This forces kids to think more about what they are doing.Finally, John distorts the image by holding out one side of the screen, orby moving the projector so that it doesn't aim perpendicular to the screen,and starts talking about what has to be true for two things to be similar(I'm fuzzier on the details of what he says here).I hope someone finds this inspirational, and I'd love to hear what personaltwists you put on it.--------------------------------------------------------Tom McDougal  (mcdougal@cs.uchicago.edu)  (312) 702-0024
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