Question

Kira is using the figure shown to prove the Pythagorean theorem. She starts by writing the

equation (a + b)2 – 2 = 4( ab) because she knows two equal ways to represent the area
of the shaded region. Which best describes the next steps Kira should take to complete her
proof?

Answer 1

It’s B

Explanation:

I did the test

Answer 2

B. Simplify both sides of the equation to get
`a^2 + 2ab + b^2 - c^2 = 2ab`; then subtract 2ab and add
`c^2` to both sides of the equation

Explanation:

Given

`(a + b)^2 - c^2 = 4((1)/(2)ab)`

Required

Describe the next steps to

First, we open all brackets

`(a + b)^2 - c^2 = 4((1)/(2)ab)`

`(a + b)(a + b) - c^2 = 4((1)/(2)ab)`

`a^2 + 2ab + b^2 - c^2 = 4 * ((1)/(2)ab)`

`a^2 + 2ab + b^2 - c^2 = 2ab`

At this point, options A and C are incorrect because they didn't present the right result of the expression.

So, we have options B and D to consider

The next step is to subtract 2ab from both sides

`a^2 + 2ab + b^2 - c^2 - 2ab = 2ab - 2ab`

Collect like terms

`a^2 + b^2 - c^2 +2ab - 2ab = 2ab - 2ab`

`a^2 + b^2 - c^2 = 0`

Lastly, to prove the Pythagoras theorem, the equation has to be in form of
`a^2 + b^2 = c^2`; meaning the
`c^2` is added to both sides; See below

`a^2 + b^2 - c^2 = 0`

Add
`c^2` to both sides

`a^2 + b^2 - c^2 + c^2= 0 + c^2`

`a^2 + b^2 = c^2`

At this point, only option B completes Kira's proof