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 the
follwing technique for introducing triangle similarity, which I got from
John Benson of Evanston Twp. H.S.:

On an overhead transparency, draw a triangle whose sides are integer
lengths, say 3cm, 4cm, 5cm.

Carefully position the overhead projector so that the projected image has
integer lengths, say 30 in., 40 in., 50 in.

Place a clear ruler alongside one of the sides of the triangle on the
overhead. Ask the class, "How long is that side?"

Inevitably some kid will say, "3 cm." Smile, then point to the projected
image: "*THAT* is 3 cm?" Measure the (projected) side, repeat for other
sides, 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 in

Then John moves the projector a little bit so that the projected sides are
no longer such nice multiples of the original, and goes through the process
again. This forces kids to think more about what they are doing.

Finally, John distorts the image by holding out one side of the screen, or
by 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 personal
twists you put on it.

Tom McDougal ( (312) 702-0024