The following proof = ofthe Pythagorean Theorem is attributed to Congressman (later President) James A Garfield; who published it in the New England Journal of Edu- cation in 1876 Let AABC be given with right angle at A. On hypotenuse BC construct "half: square, LBCE,that is, construct right angle ZBCE such that BC CE. Con- struct perpendicular from E to AC,and let the intersection be D, as illustrated in Figure Figure 7.38. Exercise 7.6.9: James Pythagorean Theorem Garfield's proof of the Prove that AABC 2 ADCE Explain why quadrilateral BADE is trapezoid Find the area of trapezoid BADE in two different ways: first; by using the area formula for trapezoid, and second, by decomposing the trapezoidal area into the sum of the areas of its three component triangles From this, prove the Pythagor- ean Theorem_