In this session, you will look at a few proofs and several applications of one of the most famous theorems in mathematics: the Pythagorean theorem. Proof is an essential part of mathematics, and what separates it from other sciences. Mathematicians start from assumptions and definitions, then follow logical steps to draw conclusions. If the assumptions are correct and the steps are indeed logical, then the result can be trusted and used to prove further results. When a result has been proved, it becomes a theorem.

For information on required and/or optional materials for this session, see Note 1.

Part A:	The Pythagorean Theorem
Part B:	Proving the Pythagorean Theorem
Part C:	Applications of the Pythagorean Theorem
Homework

In this session, you will learn how to do the following:

Examine different formal proofs of the Pythagorean theorem

Examine some applications of the Pythagorean theorem, such as finding missing lengths

Learn how to derive and use the distance formula

Throughout the session you will be prompted to view short video segments. In addition to these excerpts, you may choose to watch the full-length video of this session.

Previously Introduced

New in This Session:

altitude
perpendicular bisector
right triangle
side-angle-side (SAS) congruence

converse
coordinates
hypotenuse
Pythagorean theorem
theorem

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