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What is the Pythagorean Theorem?
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The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).
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Can the Pythagorean Theorem be used for all triangles?
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No, it can only be used for right-angled triangles.
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How do you find the length of the hypotenuse?
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To find the hypotenuse, use the formula: c = √(a² + b²), where a and b are the lengths of the other two sides.
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What types of triangles are applicable with the Pythagorean Theorem?
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Only right-angled triangles are applicable.
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If one leg of a right triangle is 3 and the other is 4, what is the hypotenuse?
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The hypotenuse is 5, since 3² + 4² = 9 + 16 = 25, and √25 = 5.
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Can the Pythagorean Theorem be applied to find a missing side when only two sides are known?
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Yes, if you know the hypotenuse and one leg, you can find the other leg using a² = c² - b² (or b² = c² - a²).
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What is a real-life application of the Pythagorean Theorem?
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The theorem is used in construction and navigation to calculate distances.
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How do you verify a triangle is a right triangle using side lengths?
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Check if a² + b² = c² holds true for the side lengths given.
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What is the converse of the Pythagorean Theorem?
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If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is right-angled.
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Can you use the Pythagorean Theorem for three-dimensional shapes?
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The basic Pythagorean Theorem applies to 2D but extensions like the 3D distance formula use similar concepts.
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What is the Pythagorean triple?
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A set of three positive integers a, b, and c that satisfy the equation a² + b² = c² is called a Pythagorean triple.
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Give an example of a Pythagorean triple besides 3, 4, 5.
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The set (5, 12, 13) is another Pythagorean triple.
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Why is the Pythagorean Theorem important in geometry?
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It helps in calculating distances and is fundamental in trigonometry and algebra applications.
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How does the theorem apply to coordinate planes?
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To find the distance between two points, apply the Pythagorean Theorem to the differences in x and y coordinates.
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What historical cultures have used the Pythagorean Theorem?
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The theorem was used by ancient Babylonian and Chinese mathematicians, aside from Pythagoras.
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