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
.