Question

GEOMETRY PROOF HELP!

I need help 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

Answer 1

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.