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DarlingDare

  • 2 years ago

Given: Square with side c. All four interior triangles are right triangles. All four interior triangles are congruent. The interior quadrilateral is a square. Prove: a2 + b2 = c2 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 ab. (1) The length of a side of the interior square is (a – b). (2) The area of all four triangles will be represented by 4 • ab or 2ab.

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  1. DarlingDare
    • 2 years ago
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    (3) The area of the interior square is (a – b)2. (4) By distribution, the area is a2 – 2ab + b2. 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), (4) to complete the proof? (2), (1), (4), (3) (1), (2), (3), (4) (1), (2), (4), (3) (2), (1), (3), (4)

  2. DarlingDare
    • 2 years ago
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    Is it the fourth one?

  3. DarlingDare
    • 2 years ago
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    I just need a confirmation... because the last one makes the most sense to me.

  4. annas
    • 2 years ago
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    yes your guess is absolutely right :)

  5. annas
    • 2 years ago
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    4 one is the answer

  6. DarlingDare
    • 2 years ago
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    Thank you!!!! :)

  7. annas
    • 2 years ago
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    welcome

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