Question

Given: A ABC is a right triangle 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 a’ and the area of the square with Prove: a + b = c² (Pythagorean Theorem) Proving which of the following will prove the Pythagorean Theorem? When you subtract the area of the smallest square from the medium square the difference equals the area of the largest square The sides of a right triangle are also the sides of squares. m2.4 m/B = mxo

Answer 1

The triangle formed by the boxes is a right angle triangle. Recall,

Area of square = length^2

The length of the sides of the given traingle are

a = opposite side

b = adjacent side

c = hypotenuse

The pythagorean theorem is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

This means that

c^2 = a^2 + b^2

The length of each side of the smallest square is a. Thus, it's area is a^2

The length of each side of the medium square is b. Thus, it's area is b^2

The length of each side of the largest square is c. Thus, it's area is c^2

Thus, in proving the pythagorean theorem,

when the sum of the area of the small and medium squares equal the area of the largest square., then the pythagorean theorem is proven