Pythagoras Similarly

There are hundreds of proofs of Pythagoras Theorem.

This diagram shows a proof.

Look carefully. Can you see three squares?

Assuming that they are squares, can you prove that four of the triangles are congruent?

Can you now write down a proof of Pythagoras’ Theorem and explain the proof?

The second diagram shows a well known proof using similar triangles.

Angle ACB is a right angle and CH is perpendicular to AB.

Explain why the two angles labelled \theta must be equal.

Explain why b^2 = dc \quad  (1).

Explain why a^2 = ec  \quad (2).

Combine equations (1) and (2) to give a proof of Pythagoras Theorem.

The AIMSSEC Inclusion and Home Learning Guide has the theme JIGSAW Proofs. It provides jigsaw tasks suitable for all ages from 5 to 18+. The youngest learners can enjoy doing the jigsaws and learn from talking about the shapes and their properties. Older learners be asked to give explanations and proofs.

Click here  for the PYTHAGORAS SIMILARLY Inclusion and Home Learning Guide.

Click here for the PYTHAGORAS SIMILARLY worksheet.

Click here for Notes for Teachers.