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Choose the correct reason to justify each of the first four statements in the derivation.

1) [tex]a^2 = h^2 + x^2[/tex]

Sagot :

GinnyAnsweridn
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.
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