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These first three questions are "warm-ups", designed to introduce the idea. You are welcome to make use of Pythagoras's Theorem as you answer them.
In the following questions, the right-angled triangle has the specific side lengths $6$, $8$ and $10$. Would your answers still be correct if we replaced them with other side lengths, say $a$, $b$ and $c$?
In this final question, you are asked to use the ideas you have learnt in the earlier questions to prove Pythagoras's Theorem. You may not assume Pythagoras's Theorem to be true when you answer this one!
In the left figure below, the blue and green regions have been formed by dropping a perpendicular as shown. How are their areas related to the red area in the right figure?
How does this result prove Pythagoras's Theorem?