Proofs for ‘Lines and Points’

The last session (Episode 3) was all about triangles. Detailed proofs of most of the results were omitted in the talk because there was not time. I have, at last, posted all the proofs on the webpage for Episode 3 – you will see why we omitted them – they are a bit long! I’ll be more than happy to explain further if you have any (even the simplest!) questions (or corrections/omissions). But they are only 2 pages long (each one).

It’s hard to know quite how surprised we should be about lines being concurrent, and points being collinear, in the study of triangles (and in many other contexts). But when we do get a surprise it’s natural to ask ‘Can we prove it?’, meaning, ‘Can we prove this will always happen in any triangle?’. If it’s a while since you’ve looked at any proofs, I recommend the ‘Centroid’ one – go straight to the Theorem (page 2) and look back at the Lemmas if you need or wish. It involves two examples of reasoning about a pair of similar triangles, so it is a mixture of concepts and logic – good preparation for thinking about proofs in the next episode.

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