There are 3 shaded squares with sides a, b, and c, respectively.
a, b, and c are also the lengths of the sides of the right triangle, such that the area of the square with side a is a2 and the area of the square with side b is b2 and the area of the square with side c is c2.
Prove: a2 + b2 = c2 (Pythagorean Theorem)
Proving which of the following will prove the Pythagorean Theorem?
A.
When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square.
B.
The sides of a right triangle are also the sides of squares.
C.
m<A+m<B=m<C
D.
The area of the two smaller squares will add up to the area of the largest square.
A.
When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square.
This statement is the direct mathematical representation of the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Therefore, proving this statement will prove the Pythagorean Theorem.