What’s the longest pencil that can fit in this box? What’s the largest computer screen that can fit in this small cubicle? These and many other real world applications may require the Pythagorean Theorem to solve.


In this activity, students will encounter proof of the Pythagorean Theorem, and use the Pythagorean theorem and its converse to solve problems. For many students, this is the first time they will encounter a “proof;” something they will get plenty of when they get to high school geometry. Incidentally, there are a number of different ways to prove the Pythagorean theorem–we show a couple of proofs in this activity. Students will also get a lot of practice solving problems in both two- and three-dimensions.

Click here to try: Applying Pythagorean Theorem to Solve Problem in Three Dimensions

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