Investigate the three triangles (where there is a single thickness of the paper) that are formed by folding in this way.
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Investigating proofs of Pythagoras Theorem by similar triangles and practical jig-saw methods. Extension to the Cosine Rule.
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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 .