Understanding Pythagorean Theorem and Special Triangles

This video tutorial covers the Pythagorean Theorem as part of the Grade 8 mathematics curriculum. It explains the theorem's formula, c² = a² + b², and demonstrates how to apply it to find the hypotenuse or other sides of a right triangle. The tutorial includes example problems, introduces the concept of Triple Pythagorean for easier calculations, and discusses special triangles like the isosceles right triangle and 30°-60°-90° triangle. The video concludes with a summary and encourages viewers to engage with the content.

What is the formula for the Pythagorean Theorem?

• a² + b² = c

• c² = a² + b²

• a² = b² + c²

• b² = a² + c²

In a right triangle, which side is the hypotenuse?

• The shortest side

• The side adjacent to the right angle

• The side opposite the right angle

• Any side

If a right triangle has legs of 5 cm and 12 cm, what is the length of the hypotenuse?

• 10 cm

• 13 cm

• 15 cm

• 17 cm

What is a Pythagorean Triple?

• A set of three numbers that are the sides of any triangle

• A set of three numbers that satisfy a² + b² = c²

• A set of three numbers that are all equal

• A set of three numbers that form an isosceles triangle

Which of the following is a Pythagorean Triple?

• 6, 8, 10

• 7, 8, 9

• 3, 4, 5

• 5, 5, 5

In a 45°-45°-90° triangle, how is the hypotenuse related to the legs?

• It is half the length of one leg

• It is the square root of 2 times the length of one leg

• It is twice the length of one leg

• It is equal to the length of one leg

In a 30°-60°-90° triangle, what is the length of the side opposite the 30° angle if the hypotenuse is 10 cm?

• 5√3 cm

• 10 cm

• 5 cm

• 10√3 cm

In a 30°-60°-90° triangle, what is the length of the side opposite the 60° angle if the shortest side is 4 cm?

• 4 cm

• 4√3 cm

• 8 cm

• 8√3 cm

If the hypotenuse of a 45°-45°-90° triangle is 10 cm, what is the length of each leg?

• 5 cm

• 10 cm

• 10√2 cm

• 5√2 cm

What should you do to better understand Pythagorean Triples?

• Search for resources online

• Use a calculator for every problem

• Ignore them

• Memorize the entire list