Double-click on the movie to PLAY.

Click once to PAUSE.

RELOAD the page or double-click to return to the START of the movie.

Method B2

It is worth scrutinising this initial configuration carefully before running the movie:
• ABC is 'any' triangle
• AB = AG = AB'
• AC = AE = AC'
• rectangles AEHB' and AGJC' are congruent and so have the same area.

As the movie runs, we can interpret rectangle AEH'B" as a stretched (or shrunk) version of AEHB', and rectangle AGJ'C" as a stretched version of AGJC'; the same stretch factor, F, is applied to each, where F = AB"/AB' = AC"/AC'.

The original rectangles have the same area, so the stretched rectangles have the same area,
so we can say AB''.AE = AC".AG, ie AB".AC = AC".AB or, using the notation on the previous page, AD.AC = AE.AB.

This is a powerful relation - we use it in the next Maths Medicine task (GEOnn) to analyse the transformation of inversion.

In the movie on the next page, we extend the animation by letting B" and C" move beyond A.
Meanwhile, you can explore the current configuration further using this interactive JAVA worksheet.