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.

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.

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

Answer 1

(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

@ganeshie8 some help please?

Answer 3

length of inner side = (a - b)

Answer 4

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

Answer 5

so 3 is first?

Answer 6

yes it starts with the length of square

Answer 7

side

Answer 8

then area of square

Answer 9

then 1?

Answer 10

(3) , (4)

Answer 11

then we can distribute (a-b)^2
so it will be (3) , (4), (2)

Answer 12

Oh, okay. Im not very good at proofs, so I always get confused. Thank you.

Answer 13

lastly area of outer square (1)

then we can equate both and simplify

Answer 14

no poblem.. wc !(:

Answer 15

already solved ;)