Square with side c.
All four interior triangles are right triangles.
All four interior triangles are congruent.
The interior quadrilateral is a square.
a2 + b2 = c2
When written in the correct order, the sentences below create a paragraph proof of the Pythagorean Theorem using the diagram.
Let a represent the height and b represent the base of each triangle.
The area of one triangle is represented by the expression One halfab.
(1) The area of the interior square is (a – b)2.
(2) The length of a side of the interior square is (a – b).
(3) By distribution,
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(3) By distribution, the area is a2 – 2ab + b2.
(4) The area of all four triangles will be represented by 4 • One half ab or 2ab.
The area of the exterior square is found by squaring side c, which is c2, or by adding the areas of the four interior triangles and interior square, 2ab + a2 – 2ab + b2.
Therefore, c2 = 2ab + a2 – 2ab + b2.
Through addition, c2 = a2 + b2.
Which is the most logical order of statements (1), (2), (3), and (4) to complete the proof?
a. (4), (1), (2), (3)
b. (4), (2), (1), (3)
c. (4), (2), (3), (1)
d. (4), (1), (3), (2)