Question

Given: △ABC is a right triangle There are 3 shaded squares with sides a, b, and c, respectively. Prove: a^2 + b^2 = c^2 (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.

Answer 1

To prove the Pythagorean Theorem, one must show that the sum of the areas of the two smaller squares, based on the lengths of the legs of a right triangle, is equal to the area of the largest square, based on the length of the hypotenuse. The correct choice is D.

Step-by-step explanation:

The question is asking which statement would prove the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c). This is mathematically represented as a2 + b2 = c2.

The correct statement that proves the Pythagorean Theorem is:

• D. The area of the two smaller squares will add up to the area of the largest square.

This means if you have a right triangle with sides a and b, and hypotenuse c, then creating squares on each of these sides will result in the areas of the smaller two squares (a2 and b2) adding up to the area of the largest square (c2).

To better understand this, consider three squares with sides equal to the lengths of the triangle's sides. The area of the first square with side 'a' is a2, the area of the second square with side 'b' is b2, and the area of the third square with side 'c' is c2. According to the Pythagorean Theorem, a2 + b2 should be equal to c2, and this is true for all right-angled triangles.