Dissected proof

Before beginning this activity it is advisable to review the concept of similarity. Students should be familiar with proving that triangles are similar and using the proportion statements. One good way to prepare is to try a simple similarity problem.

Prepare a set of cards for Proving Pythagoras' theorem for each pair of students. The cards hold either one line of the proof or a reason. Each student also receives a half-page which has the enunciation of Pythagoras' theorem and the necessary diagrams.

Students then use similarity to prove Pythagoras' theorem. Provide individual feedback to the students and check that the lines of their reasoning are correct.

If students experience difficulty you could suggest that they:

• separate the lines of data from the reasons
• focus on proving \(\triangle\)ABC and \(\triangle\)ADC similar first
• arrange the algebraic pieces in order.

When the students have produced a correct Pythagoras' similarity proof, they return the cards and then write the proof without the aid of the pieces.

This activity can be made into a permanent resource for the faculty:

1. Copy each set of solution pieces onto coloured cardboard. Having each set on a different colour of card will aid in sorting the pieces when they become separated.
2. Laminate the page of proof lines and then cut the pieces out.
3. Store each set in a small plastic bag and then store the class set in a larger container.
4. Include a master copy of the diagram page and a copy of the solution in the container.