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Proving Pythagoras' theorem
Before doing this activity it is wise to create a geometry toolkit comprising a list of basic theorems and accepted abbreviations.
Students can explore a virtual demonstration of the theorem which uses knowledge of plane shapes. Other ways to prove Pythagoras’ theorem include the use of area, algebra, congruence and similarity.
In small groups, students can research a variety of internet links such as Pythagoras' theorem proofs or Pythagoras' theorem video (see below) to find and understand at least two alternative proofs.
They can then report back to their peers what they have learned by:
- explaining a proof to another group
- cooperatively writing up a proof
- creating a physical model of a proof.
Students might also discover that Pythagoras was not the first to demonstrate this particular relationship!
In this activity, students reconstruct a proof of Pythagoras' theorem based on similarity. Students arrange a set of cards, each with either one line of the proof or a reason, in the correct order.
When students write deductive proofs in geometry they need to draw on a significant store of knowledge and skills which they have acquired over a number of years.