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

Answer 1

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1002_01/1002_01_02.jpg

Answer 2

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.

(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?

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

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

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

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

Answer 3

Is it the last one?

Answer 4

I think it's the second one because you first have a side, then you get the formula, then you set it up, then you get the area I believe.

Answer 5

Not completely sure though...

Answer 6

Okay so I looked up what other people said for the same question on OpenStudy...they were mixed but some of them said that D was correct...

Answer 7

Alright. If you want go ahead with it.

Answer 8

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