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Perpendicular Lines & Gradients

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From: Teo
To: Teacher2Teacher Service
Date: Nov 01, 1998 at 09:56:26
Subject: Perpendicular Lines & Gradients

I'm a secondary school maths teacher. All these years I've been teaching my 
students the property m1.m2 = -1 for two perpendicular lines using the 
following methods:
(1) Showing them many concrete examples by asking them to actually draw the 
lines and make the required inference;
(2) From two perpendicular lines drawn on the Cartesian Plane, and using 
the result m1 = tan@, m2 = -tan(90-@) = -cot@, whereby the result m1.m2=-1 
is obtained;
(3) by using the formula for finding the angle between two lines , i.e. 
tan(@1-@2) = [m1-m2]/[1+m1m2] 

Could someone kindly suggest other methods to teach this concept? It would 
be much better if the method involves some form of 'games', which I feel 
could bring some FUN to learning mathematics. Thanks.

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