Pythagorean theorem in 3D Description Exercise Name: Pythagorean theorem in 3D Math Missions: 8th grade (U.S.) Math Mission Types of Problems: 1

The Pythagorean theorem in 3D exercise appears under the 8th grade (U.S.) Math Mission. This exercise practices the Pythagorean theorem in three-dimensional objects.

Types of Problems

There is one type of problem in this exercise:

Find the requested length: This problem has a three-dimensional picture or drawing. The user is expected to use the Pythagorean theorem to find a requested length in the figure.

Strategies

Knowledge of the Pythagorean theorem in two dimensions and an ability to visualize in three dimensions are encouraged to ensure success on this exercise.

The Pythagorean theorem in three dimensions can be viewed as $ {a^2+b^2+c^2=d^2} $ . If the dimensions of $ {a} $ rectangular box are $ {a} $ , $ {b} $ and $ {c} $ , then $ {d} $ is the "long" diagonal of the box. The Pythagorean theorem in three dimensions is actually just the standard Pythagorean theorem performed twice.





Real-life Applications