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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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