To determine if a triangle is a right triangle, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The relevant response will depend on the specific lengths of the sides of the triangle in question. However, I can help clarify the correct response based on the general principles:
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If you have side lengths a, b, and c, with c as the longest side:
- Check if \(a^2 + b^2 = c^2\). If this equation holds true, then the triangle is a right triangle.
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If the triangle is confirmed to be right:
- You would choose a response that affirms that the Pythagorean Theorem holds true using the appropriate hypotenuse.
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If the triangle is not a right triangle:
- You would select the response that states the Pythagorean Theorem does not hold true for the given sides.
Based on the responses provided:
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If the Pythagorean Theorem holds true using 14 as the hypotenuse, you should select: "Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse."
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If it does not hold true, choose: "No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse."
If the triangle does not satisfy the Pythagorean theorem regardless of which side you consider as the hypotenuse, choose: "No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse."
The other option suggesting the theorem holds true for any of the sides is incorrect since the theorem only applies correctly in the context of right triangles.
You will need to evaluate the specific triangle side lengths to select the correct option.