Question

using the provided diagram, which of the following is a correct way to substitute the side lengths into the pythagorean theorem? h² + g² = k² g² + h² = k² two of these are correct. g² + k² = h²

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side opposite the right - angle) and $a$ and $b$ are the two legs of the right - triangle.

Step2: Identify hypotenuse and legs

In the given right - triangle, the hypotenuse is $k$ and the legs are $g$ and $h$.

Step3: Substitute into the theorem

Substituting the side lengths into the Pythagorean Theorem gives $g^{2}+h^{2}=k^{2}$. Also, since addition is commutative, $h^{2}+g^{2}=k^{2}$ is correct.

Answer:

C. Two of these are correct.