Question

Hurry please answer questions 1, 2 and 3!!! thank you!!

Answer 1

What is the Pythagorean Theorem?

The PyTheorem states that -- actually, why not just simplify things and make it a formula?

$a^{2} + b^{2} = c^{2}$
where a and b are legs of a triangle and c is the hypotenuse of a triangle.

It is only true applying to right triangles.
Now what are the legs of a triangle? 
The sides that are NOT opposite the 90 degree angle! 

Now, all you have to do is find the LENGTHS of the three triangles!
Rise over run, remember?

Let's take the triangle in the top right of the coordinate plane for example.

A=(1,1)
B=(4,4)
unnamed point=(4,1)

Rise, or length of unnamed point to B?
(4,1) to (4,4)
(x,y), remember!
So? 4-1=3!

Run, or length of unnamed point to A?
(1,1) to (4,1)
Remember (x,y)?
So, 4-1=3!

The triangle has legs of 3 and 3.
Square em and add!
9+9=18
$\sqrt{18}$
$\sqrt{3*6}$
$\sqrt{ 3^{2} *2}$
$3 \sqrt{2}$

That's for length of AB!!
Now do the same for the remaining lengths!

Hope this helps!