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 (mcdougal@cs.uchicago.edu) (312) 702-0024