Diagonal Lengths and Pythagorean Theorem

The video tutorial explains how to use the Pythagorean theorem to find distances in 3D objects, focusing on right triangles. It begins with a review of the theorem, emphasizing its application to right triangles only. The tutorial then demonstrates how to apply the theorem to find the longest diagonal in 3D shapes like cubes and rectangular prisms. Through detailed examples, the video guides students in calculating these distances, encouraging them to practice independently.

What type of triangles can the Pythagorean theorem be applied to?

• Obtuse triangles

• Isosceles triangles

• Right triangles

• Equilateral triangles

In the context of a shoebox, why might placing an object diagonally allow for a longer fit?

• It reduces the object's volume.

• It increases the object's width.

• It makes the object lighter.

• It utilizes the diagonal space, which is longer.

When finding the longest diagonal in a rectangular prism, what is the first step?

• Calculate the volume of the prism.

• Find the area of the base.

• Create two different right triangles.

• Measure the height of the prism.

What is the approximate length of the diagonal found using the Pythagorean theorem in the example?

• 5.4

• 8.3

• 6.2

• 7.1

In the final example, what is the length of the longest diagonal in the box?

• 13

• 12

• 11

• 10