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Similar Triangles to measure the height of a student…

on March 6, 2012

Well, today’s Y9 lesson was very ‘creative’…  We have been looking at similar triangles, and I found a useful resource on TES (that I now can’t find at home… will add link later).  The resource asks students to match up the shape that is similar to the one given.  It then leads on to show similar triangles like this:

Image

We discussed why they are similar (angles all the same) and that therefore one was an enlargment of the other.

We worked out the scale factor, and therefore the missing sides on a couple of examples, which was the level 8 skill I wanted them to at least try.

I then had a moment of stupidity brainwave…

We’ll measure the height of Bradley!

I got a student to lie on the floor, and positioned Bradley across the room, and the metre ruler at the correct position so that the person-on-floor(D) had lined up the top of the ruler(E) with the top of Bradley’s head(A).    We then measured the distance from person-on-floor to Bradley’s feet(BD), and from person-on-floor to the bottom of the metre ruler(CD).

I drew up the diagram (as above) on the board, and we worked out the scale factor of the base of the triangle, and used that to work out how tall Bradley was 🙂

We discussed how it might have been easier to just measure him, but that we could use the technique for other stuff that wouldn’t be so easy.

Discussion ensued about measuring the height of the Eiffel Tower etc, or simply a tree or lamppost, and how you could make it work without having to lie down on the floor too….!

Very productive lesson, and most seemed to grasp the concept well.   Hopefully they’ll remember it!

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