Question

Given:
Square with side c.
All four interior triangles are right triangles.
All four interior triangles are congruent.
The interior quadrilateral is a square.
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Answer 1

Prove:
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.

Answer 2

The area of one triangle is represented by the expression 1/2 ab.

(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, the area is a2 – 2ab + b2.

Answer 3

(4) The area of all four triangles will be represented by 4 • 1/2 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?

Answer 4

(4), (1), (2), (3)

(4), (2), (1), (3)

(4), (2), (3), (1)

(4), (1), (3), (2) ?