The Pythagorean theorem
Welcome! I am so excited to dive into the beauty of geometry with you. Before we sketch out our learning path, I'd love to learn a little bit about what brings you here today.
To help me tailor our session, could you tell me a little about your math background or why you're interested in learning about the Pythagorean theorem?
I'm just curious about how it works and want to learn for fun!
Learning math just for fun is the absolute best way to do it! There is something incredibly satisfying about watching the pieces of a geometric puzzle click together, and the is one of the most elegant puzzles in history.
Your path
Visualizing and Proving the Theorem
Applying the Theorem to Solve Problems
Real-world Applications and the Converse
To get our gears turning, we are going to start with the absolute foundation: the .
For the Pythagorean theorem to work, you must have a triangle where exactly one of the angles is a perfect 90-degree corner, just like the corner of a square piece of paper.
A right-angled 3-4-5 triangle with horizontal side a, vertical side b, and hypotenuse c.
As you can see in the diagram, the three sides of a right triangle have specific, fancy names based on where they sit:
- The Legs: The two shorter sides ( and ) that meet to form that sharp 90-degree right angle.
- The Hypotenuse: The longest side (). It is always directly across from the right angle, stretching out like a bridge connecting the two legs.