To determine whether a triangle is a right triangle, we apply 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 other two sides.
If we denote the lengths of the sides of the triangle as \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse), the theorem can be expressed as:
\[ a^2 + b^2 = c^2 \]
To answer the question of whether this specific triangle is a right triangle, you would need to know the lengths of all three sides. Based on the responses provided, here is how each option corresponds to the situation:
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Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse - This suggests that no matter which side is the hypotenuse, the relationship holds, typically indicating that all sides form a right triangle.
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Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse - This indicates that specifically when using 14 as the hypotenuse, the sum of the squares of the other two sides equals \(14^2\). If this is true, the triangle is a right triangle.
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No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse - This suggests that none of the sides satisfy the Pythagorean theorem, indicating that it is not a right triangle.
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No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse - This states that even when considering 14 as the hypotenuse, the Pythagorean theorem doesn't hold, thereby confirming it's not a right triangle.
Without additional information on the specific lengths of the sides, it's impossible to definitively conclude whether the triangle is right-angled. You would need to calculate and check the Pythagorean relationship. Based on the options given, you can select the correct response based on your calculations.