Investigating proofs of Pythagoras Theorem by similar triangles and practical jig-saw methods. Extension to the Cosine Rule.
Click here to download a pdf with all you need to run your own professional development workshop.
Find the total area of the two triangles by two different methods if ACD and BCE are straight lines .
What are the lengths PC and CQ?
The triangles are re-drawn keeping the total area the same and keeping the distances between the green parallel lines as 3 cm and BD = 4 cm.
The squares in the diagram are to help us visualise an infinite geometric sum and we are not summing the areas of the squares, simply the lengths along the x-axis. The squares have side lengths given by powers of r: where 0 < r < 1 .
Investigate the three triangles (where there is a single thickness of the paper) that are formed by folding in this way.
Click here for […]