Question

In the diagram below, all four right triangles are congruent and the interior quadrilateral is a square. (con.)

Answer 1

In the diagram below, all four right triangles are congruent and the interior quadrilateral is a square.



When written in the correct order, the paragraph below proves 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 onehalf_largeab.

The area of all four triangles will be represented by 4 • onehalf_largeab or 2ab.

(1) 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.

(2) By distribution, the area is a2 – 2ab + b2.

(3) The length of a side of the interior square is (a – b).

(4) The area of the interior square is (a – b)2.

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?

Answer 2

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Answer 3

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Answer 4

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Answer 5

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Answer 6

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