Understanding Diagonals in a Cube

The video tutorial explains how to find the length of a diagonal on a cube. It begins by introducing the concept and drawing a diagonal across the face of a cube. The instructor then isolates a right triangle and applies the Pythagorean theorem to find the diagonal's length. Additionally, the video covers the shortcut rules for a 45-45-90 triangle, which simplifies the calculation of the hypotenuse when the legs are known. The tutorial concludes with a practical example of calculating the hypotenuse using these methods.

What is the first step in finding the diagonal of a cube?

• Draw a diagonal across the face of the cube

• Calculate the volume of the cube

• Measure the side length of the cube

• Find the area of the cube's face

Which theorem is used to find the diagonal across the face of a cube?

• Fundamental theorem of calculus

• Binomial theorem

• Remainder theorem

• Pythagorean theorem

What type of triangle is formed when isolating a triangle on the cube's face?

• Isosceles triangle

• Scalene triangle

• Right triangle

• Equilateral triangle

What is the shortcut rule for finding the hypotenuse in a 45-45-90 triangle?

• Multiply the leg by 2

• Multiply the leg by 1.5

• Multiply the leg by the square root of 3

• Multiply the leg by the square root of 2

If each leg of a 45-45-90 triangle is 6, what is the length of the hypotenuse?

• 6√3

• 12

• 6√2

• 6

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

• The hypotenuse is twice the leg

• The hypotenuse is equal to the leg

• The hypotenuse is the leg divided by 2

• The hypotenuse is the leg multiplied by the square root of 2