Geometry proof ! i need with the rest of the blanks in the picture. given: abc is a right triangle, with right angle at c. prove: a^2 + b^2= c^2

Picture a square with sidelength a+b. Now, draw another square of sidelength c wedged inside the previous square with points that split each side of the big square into length a and b.

The area of the big square would be (a+b)^2, which simplifies to a^2 + 2ab + b^2.

However, the area of the big square can also be found by adding the area of the small square to the area of the four small right triangles with legs a and b.

This method would turn out to be c^2 + 4(ab/2), which simplifies to c^2 + 2ab. Remember, this is equal to a^2 + 2ab + b^2. So,

c^2 + 2ab = a^2 + 2ab + b^2.

Subtracting 2ab from both sides, we get c^2=a^2+b^2.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)