Perigal's dissection proof of Pythagoras' Theorem (Geometry I Exercise 5.5 1-4)

Perigal produced a proof of Pythagoras' Theorem that indicates how to dissect one of the squares on the sides of a right triangle into four quadrilaterals and then use these quadrilaterals and the smaller square to cover the larger square.

If possible rearrange the smaller square and the 4 quadrilarterals to cover the large square on the hypotenuse. If the 5 pieces exactly cover the larger square, then this provides a demonstration of Pythagoras' Theorem by means of dissection.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

1. Why is M the midpoint of segment PQ?

2. Why is the length of PQ = length of AB?

3. Why is the length of BQ - length of CP = length of AC?

4. Why are the four quadrilaterals congruent?

Kelly Harms, Created with GeoGebra