Question

Need someone to check my answers.

Answer 1

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 One halfab.

(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 • One halfab or 2ab.

(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)

Answer 2

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 3

I got C

Answer 4

@phi

Answer 5

which choice is C ?

Answer 6

1,2,4,3

Answer 7

They start off saying
Let a represent the height and b represent the base of each triangle.

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

I think the next statement should finish that thought:
(2) The area of all four triangles will be represented by 4 • (1/2) ab or 2ab.

that sound reasonable ?

Answer 8

yeah

Answer 9

you now have 3 statements left

(1) The length of a side of the interior square is (a – b).
(3) The area of the interior square is (a – b)2.
(4) By distribution, the area is a2 – 2ab + b2.

It seems clear (to me, anyways) that you need to define the length of the side of the square before you can find the area. So (1) comes next

the area is side*side or side^2, so (3) makes sense
finally (4), because you can expand (a-b)^2 to get a^2 -2ab+b^2

Answer 10

after that, they say


adding the areas of the four interior triangles and interior square, 2ab + a2 – 2ab + b2.


so they are using step (4) results. So (4) definitely comes after step 3

Answer 11

So 1234?

Answer 12

read over what I posted.

Answer 13

It definitely 2134 correct?