The Pythagorean Theorem: Why a² + b² = c² Works

The Pythagorean theorem is not just a formula to memorize. In a right triangle, the squares on the two legs have areas that add to the area of the square on the hypotenuse. This lesson builds that picture first, then uses it to solve missing-side problems and to spot when the theorem should not be used. By the end of this lesson you can: • Identify the hypotenuse of a right-angled triangle and state a-squared plus b-squared equals c-squared with c on the hypotenuse • Explain the theorem as an equality of the areas of squares built on the three sides • Find a missing hypotenuse or leg from the other two side lengths, using a square root only after the squared length has been found • Decide whether the Pythagorean theorem applies and use size reasoning to reject implausible side lengths Chapters 00:00 See the theorem as square areas 00:26 What you will learn 01:09 Find the hypotenuse 01:38 Why a² + b² = c² works 02:25 Orientation does not change the hypotenuse 02:51 Worked example: find the hypotenuse 03:35 Worked example: find a leg 04:05 When the theorem does not apply 05:04 Quiz 06:40 Quiz answers and explanations 07:37 Homework 08:07 Recap and coordinate-distance connection Playlist: Geometry Homework answers are posted in the comments.