Question

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 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.

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

(4) By distribution, the area is a2 – 2a

Answer 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.

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

Answer 2

From what I see, I believe the order would be 1,3, 2, 4, but that isn't a choice so I'm confused.

Answer 3

What does 4th point mean?

Answer 4

(4) By distribution, the area is a2 – 2ab + b2.
It must not have sent correctly, sorry.

Answer 5

np:)

Answer 6

I think u r right; but what is the correct ans.

Answer 7

I'm not sure. I think I'm just going to call my teacher later and hope she answers. I'm having trouble with two others though. Do you think you could help?

Answer 8

ya wait a min. please:)

Answer 9

I think now that (2),(1),(3),(4) should be right:)

Answer 10

That's also what I originally thought, but I'm still going to talk to her. Thanks for your help!

Answer 11

yw:)

Answer 12

I have thought this answer bcoz 2nd point is different from others and we know this point at first sight.k!
Then we think about internal square's side & go on continuously for its area& then put the results together to prove Pythagorean theorem:)

Answer 13

Okay! Thanks so much!

Answer 14

yw:)