Common stuff

Question 1

What is a Pythagorean triple?

Answer 1

A set of three positive integers a, b, and c such that a² + b² = c².

Question 2

Which of the following is a common Pythagorean triple? A) (5, 12, 13) B) (7, 24, 25) C) (8, 15, 17) D) All of the above

Answer 2

D) All of the above

Question 3

True or False: The Pythagorean triple (6, 8, 10) is derived from the multiples of the triple (3, 4, 5).

Answer 3

True

Question 4

Fill in the blank: The smallest Pythagorean triple is _____

Answer 4

(3, 4, 5)

Question 5

What is the relationship between the sides in a Pythagorean triple?

Answer 5

The sum of the squares of the two shorter sides equals the square of the longest side.

Question 6

List one example of a Pythagorean triple that includes the number 9.

Answer 6

(9, 12, 15)

Question 7

Which Pythagorean triple corresponds to the sides of a 45-45-90 triangle?

Answer 7

(1, 1, √2)

Question 8

True or False: All Pythagorean triples consist of even numbers.

Answer 8

False

Question 9

What is the formula to generate a Pythagorean triple using two positive integers m and n?

Answer 9

(m² - n², 2mn, m² + n²)

Question 10

Identify one property of all Pythagorean triples.

Answer 10

At least one of the numbers in a primitive Pythagorean triple is odd.