Understanding Pythagorean Triples

The video tutorial explains Pythagorean triples, sets of three numbers that satisfy the Pythagorean theorem (a² + b² = c²). It provides examples to illustrate how to determine if a set of numbers forms a Pythagorean triple, which indicates a right-angled triangle. The video includes two example problems, demonstrating the process of verifying Pythagorean triples and concludes with a recap of the steps involved.

What is a Pythagorean triple?

• A set of three numbers that are all even

• A set of three numbers that satisfy the equation a^2 + b^2 = c^2

• A set of three numbers that are all prime

• A set of three numbers that are consecutive integers

Which of the following sets of numbers is a Pythagorean triple?

• 7, 8, 9

• 5, 6, 7

• 3, 4, 5

• 2, 3, 4

How can Pythagorean triples help in identifying a right-angled triangle?

• They can determine the area of the triangle

• They can calculate the perimeter of the triangle

• They can confirm if the triangle is isosceles

• They can verify if the triangle has a 90-degree angle

In the example with sides 9, 40, and 41, what is the hypotenuse?

• None of the above

• 40

• 41

• 9

What is the result of 9 squared plus 40 squared?

• 1681

• 1441

• 1521

• 1600

In the second example, what is the length of side c?

• 22

• 20

• 12

• 16

What is the sum of 12 squared and 16 squared in the second example?

• 144

• 256

• 484

• 400

Why do the numbers 12, 16, and 22 not form a Pythagorean triple?

• Because they are not all even

• Because they are not consecutive numbers

• Because 12 squared plus 16 squared does not equal 22 squared

• Because they are not all prime

What is the correct conclusion if a set of numbers does not satisfy the Pythagorean theorem?

• The triangle is scalene

• The triangle is isosceles

• The triangle is not right-angled

• The triangle is equilateral

What is the first step in determining if three numbers form a Pythagorean triple?

• Ensure the numbers are in ascending order

• Check if the numbers are all even

• Write out the Pythagorean theorem

• Calculate the perimeter of the triangle