Flash Cards: The Baudhayana-Pythagoras Theorem
The Baudhayana-Pythagoras Theorem - Flash Cards
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What is the Baudhayana-Pythagoras Theorem?
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The Baudhayana-Pythagoras 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. Mathematically, a² + b² = c².
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What does 'hypotenuse' refer to?
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In a right triangle, the hypotenuse is the side opposite the right angle, and it is the longest side of the triangle.
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3/19
How can you construct a square with double the area of a given square?
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To construct a square with double the area, draw a square on the diagonal of the original square. The new square will have an area that doubles the original.
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4/19
What is the formula for the area of a square?
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The area of a square is calculated as A = side².
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If a square has a side length of 'a', what is the area?
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The area of the square is a².
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What happens to the area when the side length of a square is doubled?
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If the side length is doubled from 'a' to '2a', the new area is (2a)² = 4a², which is four times the original area.
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How do you halve the area of a square?
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To halve the area, construct a smaller square inside the original square. The side length of the smaller square should be √(original area / 2).
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What is the relationship between a square's diagonal and its area?
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The area of the square on the diagonal c is given by c² = 2a² if 'a' is the side of the original square.
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What is the decimal representation of √2?
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The decimal representation of √2 is approximately 1.41421356..., a non-terminating decimal.
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Why is √2 not a fraction?
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√2 cannot be expressed as a fraction because it is an irrational number, as proven by the contradiction in its prime factors.
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What are Baudhāyana triples?
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Baudhāyana triples are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c², forming the sides of a right triangle.
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Can you name some Baudhāyana triples?
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Some Baudhāyana triples include (3, 4, 5), (5, 12, 13), and (8, 15, 17).
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What is the significance of the hypotenuse in a right triangle?
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The hypotenuse is crucial as it relates to the other two sides through the Pythagorean theorem, used in many geometry applications.
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How can you find the hypotenuse using side lengths a and b?
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You can find the hypotenuse using the formula c = √(a² + b²).
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What defines a primitive Baudhāyana triple?
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A primitive Baudhāyana triple has no common factor other than 1 among its elements a, b, and c.
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What are 'non-primitive' Baudhāyana triples?
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Non-primitive Baudhāyana triples have at least one common factor other than 1, like (6, 8, 10), which can be reduced to the primitive triple (3, 4, 5).
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What generalization can be made about Baudhāyana triples?
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If (a, b, c) is a Baudhāyana triple, then (ka, kb, kc) is also a Baudhāyana triple for any positive integer k.
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What process helps to combine two different squares?
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To combine two different squares, form a right triangle from their sides. The hypotenuse square's area equals the sum of the two smaller squares' areas.
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How is congruence relevant to triangle properties?
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Congruence in triangles indicates that triangles are equal in shape and size, crucial for proving theorems like the Pythagorean theorem.
