Garfield Proof

Looking at the diagram, there are several givens:

• Triangle ABC is a right triangle with hypotenuse AB.
• Segment BD is congruent to segment AC.
• Segment DE is parallel to segment AC and segment DE is congruent to segment CB.

Steps of the proof:

• Let segment AC = b, segment CB = a, and Segment AB = c. Then let segment BD = b, segment DE = a, and segment BE = c.
• Find the area of the trapezoid.
  A(trapezoid) = .5(a + b)(a + b) = .5(a + b)^2
• Find the area of the three triangles.
  A(triangles) = .5ab + .5ab + .5c^2
  
• Set the area of the trapezoid equal to the area of the three triangles and simplify.
  .5(a + b)^2 = .5ab + .5ab + .5c^2
  (a + b) ^2 = ab + ab + c^2
  (a + b)^2 = 2ab + c^2
  a^2 + 2ab + b^2 = 2ab + c^2
  a^2 + b^2 = c^2