# Pythagoras theorem proof questions....?

James Garfield (1831-1881): American politician who's hobby were mathematics, became the chief of the Republican party in 1876. He was elected president of the United States in November 1880. According to the American constitution, he started his duty in January 1881 but was assassinated 2 months later. One... show more James Garfield (1831-1881): American politician who's hobby were mathematics, became the chief of the Republican party in 1876. He was elected president of the United States in November 1880. According to the American constitution, he started his duty in January 1881 but was assassinated 2 months later.

One day he decided to find a proof of the Pythagoras theorem: a² + b² = c².
Garfield has the idea to draw a trapezium with 2 right angles of sides a, b & c, and a right isosceles triangle with 2 sides equal to c. Here is how he proceeded:

1. Calculate the area of the trapezium by 2 ways using a, b & c.

2. Write an equation using the 2 formulae you have just found.

3. Simplify the equation and conclude.