Pythagorean Theorem

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1. The Pythagorean theorem was named after Pythagoras, who was a Greek mathematician and philosopher. The theorem states that for a right-angled triangle, the sum of the squares of the 2 shorter sides is equal to the square of length of the longest side. Let a and b denote the 2 shorter sides and c denote the longest side. Hence, this theorem can be represented by which of the following mathematical equations? (a + b)^2 = c^2 a^2 + b^2 = c^2 a^2 = b^2 + c^2 (a + c)^2 = b^2

2. The longest side of a right-angled triangle is the side opposite the right angle. By using the Pythagorean theorem, the length of the longest side can be calculated by using the formula h = square root of (f^2 + g^2), where f and g are the lengths of the two shorter sides. What is the specific mathematical term that is used to denote this longest side? Hypertangent Hypotenuse Hyperbola Hypothesis

3. In trigonometry, the Pythagorean theorem is considered as a special case derived from a law. In other words, this mathematical law is a more general formula that can be used for all types of triangles. What is the name of this law? Law of cosecants Law of cosines Law of tangents Law of sines

4. True or false: There is only one way to prove the Pythagoras theorem. True False

5. The 20th President of the United States provided an algebraic proof of the Pythagorean theorem. Who is he? James A. Garfield John F. Kennedy George Washington Abraham Lincoln

6. Given a right-angled triangle and the lengths of its three sides are 3, 4 and 5. These three positive integers are known as a Pythagorean triple denoted by (3, 4, 5), as they satisfy the equation stated by the Pythagorean theorem. If I multiply each of the number by 10, will the resulting numbers, namely 30, 40 and 50 be another Pythagorean triple? Yes No

7. There are many formulae that can be used to generate Pythagorean triples. One of them states that a = m^2 - n^2, b = 2mn, c = m^2 + n^2 form a Pythagorean triple given that three conditions are met. First, the greatest common divisor of m and n is 1; second, only m or only n can be even; and third, m must be greater than n. What is the name of this formula? Plato's formula Monet's formula Archimedes' formula Euclid's formula

8. A Pythagorean prime is any prime number that is also the length of the hypotenuse of a Pythagorean triple . The first few Pythagorean primes are 5, 13, 17, 29... What is the formula used to generate Pythagorean primes? (given that n is a subset of positive integers) 4n + 1 2n + 3 3n + 2 n + 4

9. Which of the following coordinate systems uses the Pythagorean theorem to find the distance between 2 points? Polar coordinate system Elliptic coordinate system Parabolic coordinate system Cartesian coordinate system

10. The Pythagorean theorem can only be applied to which of the following triangles? Triangle A: a triangle that is inscribed in a semicircle, where the diameter of the semicircle is its longest side Triangle B: an equilateral triangle Triangle C: a scalene triangle, with length 7, 8 and 9 Triangle D: a triangle with length 1, 1 and square root of 2 Triangle B and C Triangle A and D Triangle A and C Triangle B and D