Understanding Pythagorean Triples

The video tutorial introduces Pythagorean triples, focusing on common examples like 3, 4, 5 and 5, 12, 13. It explains how these triples satisfy the Pythagorean Theorem and demonstrates their application in solving geometric problems. The tutorial also covers how to generate new triples by multiplying existing ones by a common factor, providing a list of common triples and examples of their multiplication.

What is a Pythagorean triple?

• A set of three numbers that can form a right triangle

• A set of three numbers that are all even

• A set of three numbers that are all odd

• A set of three numbers that add up to 100

Why is the set 3, 4, 5 considered a Pythagorean triple?

• Because 3, 4, and 5 are all prime numbers

• Because 3, 4, and 5 are consecutive numbers

• Because 3 squared plus 4 squared equals 5 squared

• Because 3 + 4 = 5

If a triangle has sides 6 and 10, what is the length of the missing side using the 3, 4, 5 triple?

• 8

• 7

• 10

• 9

How do you generate a new Pythagorean triple from 3, 4, 5?

• Subtract 1 from each number

• Multiply each number by the same factor

• Divide each number by 2

• Add 1 to each number

What is the result of multiplying the 3, 4, 5 triple by 2?

• 6, 8, 10

• 15, 20, 25

• 9, 12, 15

• 12, 16, 20

Which of the following is a common Pythagorean triple?

• 7, 10, 12

• 5, 12, 13

• 8, 11, 14

• 6, 8, 9

What is the result of multiplying the 5, 12, 13 triple by 3?

• 15, 26, 39

• 15, 36, 39

• 20, 48, 52

• 10, 24, 26

Which of the following sets is not a Pythagorean triple?

• 20, 21, 29

• 7, 24, 25

• 8, 15, 17

• 9, 12, 15