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

When written in the correct order, the sentences below create a paragraph proof of 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 area of the interior square is (a – b)2.

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

(3) By distribution, the area is a2 – 2ab + b2.

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

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), and (4) to complete the proof?

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

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

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

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

Answer 2

it CANNOT start with (4)

Answer 3

makes no sense to me , check ur options once

Answer 4

That's all the choices I have

Answer 5

oops- pls disregard... it does start with (4)

Answer 6

lol will do

Answer 7

we have base of triangle = b
height = a

so we can find area of triangle, and since all four triangles are congruent, we can find area of all 4 triangles by multiplying (1/2)ab by 4
(1/2)ab * 4 = 2ab

(4),...

next what

Answer 8

we can find the side of inner-square

Answer 9

Oh

Answer 10

its (a-b)
next, area of square (a-b)^2
next.. ?

Answer 11

Not sure.

Answer 12

second statement would be length of square, right ?

Answer 13

Length?

Answer 14

You beat me...

Answer 15

lol, see the diagram, we can find length of side of square, by subtracting b from a
length = (a-b)

Answer 16

so, (2) is the correct one in the sequence

Answer 17

Yep

Answer 18

once we knw length of side of a square,

cant we find its area ?

Answer 19

Yes so then 1?