The given statement \( a^2 = h^2 + x^2 \) is derived from the Pythagorean theorem. Let me explain it step by step:
1. Understand the Context:
- You have a right triangle.
- The sides of this right triangle are:
- \(a\): The hypotenuse (the side opposite the right angle)
- \(h\): One leg of the triangle
- \(x\): The other leg of the triangle
2. Pythagorean Theorem:
- The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (\(a\)) is equal to the sum of the squares of the lengths of the other two sides (\(h\) and \(x\)).
- Mathematically, this is expressed as:
[tex]\[
a^2 = h^2 + x^2
\][/tex]
3. Reason for Justification:
- The given statement \( a^2 = h^2 + x^2 \) follows directly from the Pythagorean theorem.
- Therefore, the correct reason to justify this statement is: "The statement \( a^2 = h^2 + x^2 \) is justified by the Pythagorean theorem."
So, the correct reason to justify the first statement in the derivation is:
The statement [tex]\( a^2 = h^2 + x^2 \)[/tex] is justified by the Pythagorean theorem.
