Exploring Pythagorean Theorem and Special Right Triangles

The video tutorial covers the Pythagorean theorem, explaining its application in finding areas and its significance in right triangles. It introduces two special right triangles: the 45-45-90 and 30-60-90 triangles, detailing their properties and relationships between their sides. The tutorial includes practical examples and encourages students to explore these concepts further.

What is the formula of the Pythagorean theorem?

• A^2 * B^2 = C^2

• A^2 + B^2 = C^2

• A^2 / B^2 = C^2

• A + B = C

How does the area of the squares relate to the sides of the right triangle in the Pythagorean theorem?

• Sum of the areas of squares on the legs equals the area of the square on the hypotenuse

• Area of the square on the hypotenuse equals the sum of the squares on the legs

• Area of each square on the legs is half the area of the square on the hypotenuse

• Area of the square on the hypotenuse is double the sum of the areas of squares on the legs

In a 45-45-90 triangle, if one leg is 5, what is the length of the hypotenuse?

• 5

• 7.5

• 10

• 5√2

What is the relationship between the legs and the hypotenuse in a 45-45-90 triangle?

• Hypotenuse = leg + √2

• Hypotenuse = leg / √2

• Hypotenuse = leg - √2

• Hypotenuse = leg * √2

What is the result when the side length of a leg in a 45-45-90 triangle is 8?

• 4√2

• 8

• 16

• 8√2

In a 30-60-90 triangle, if the shorter leg is 4, what is the length of the longer leg?

• 4√3

• 8

• 12

• 16

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 6?

• 18

• 6√3

• 12

• 6√2

In a 30-60-90 triangle, if the hypotenuse is 20, what is the length of the shorter leg?

• 10

• 10√3

• 20√2

• 20√3

What is the relationship between the longer leg and the shorter leg in a 30-60-90 triangle?

• Longer leg = shorter leg * √3

• Longer leg = shorter leg + √3

• Longer leg = shorter leg / √3

• Longer leg = shorter leg - √3

If the longer leg of a 30-60-90 triangle is 9√3, what is the length of the shorter leg?

• 9

• 18

• 3

• 27