Triangle Properties and Simplifying Expressions

The video tutorial discusses the isosceles right triangle theorem, which states that in an isosceles triangle, the hypotenuse is the product of the leg length and the square root of two. The instructor provides examples to demonstrate how to calculate the hypotenuse and solve for missing sides using this theorem. The lesson concludes with a rationalization of the hypotenuse and a summary of the key points.

What does the isosceles right triangle theorem state about the hypotenuse?

• It is equal to the sum of the legs.

• It is equal to the product of the leg and the square root of two.

• It is equal to the square of the leg.

• It is equal to the leg divided by two.

In an isosceles right triangle, if one leg is x, what is the length of the hypotenuse?

• 2x

• x

• x^2

• x√2

If the legs of an isosceles right triangle are 12, what is the hypotenuse?

• 12

• 24√2

• 12√2

• 24

What is the length of the hypotenuse if the legs are 12?

• 24√2

• 12

• 12√2

• 24

In the second example, if the hypotenuse is x and the legs are 8√6, what is x?

• 8√12

• 16√3

• 16

• 8√3

What is the length of the hypotenuse if the legs are 8√6?

• 8√12

• 16

• 16√3

• 8√3

What is the result of multiplying 8√6 by √2?

• 8√3

• 16√3

• 8√12

• 16

What is the square root of 4?

• 2

• 1

• 3

• 4

What is the product of 8 and 2?

• 10

• 12

• 14

• 16

What is the result of multiplying 6 by 2?

• 16

• 12

• 10

• 14