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### Course: High school geometry>Unit 5

Lesson 2: Pythagorean theorem proofs

# Another Pythagorean theorem proof

Visually proving the Pythagorean Theorem. Created by Sal Khan.

## Want to join the conversation?

• How con we use this proof and theorem in are daily life's? I don't see how we could use it.
• The real value of teaching proof in geometry class is to teach a valuable life skill. You learn to think logically, step-by-step, to learn to distinguish what you think is true from what can be shown to be true. We call these skills "critical thinking". These skills can keep you from being deceived.

You don't have to try very hard to find an advertisement or other claim that may or may not be true. There is great advantage in having the skills to examine a claim one piece of evidence at a time until you know the claim if false or know that it is well-supported and may be true.

So, geometry is a class where the basics of that skill are taught. Will you need to know in most professions whether two triangles are congruent? No, you won't. Will you need to be able to analyze claims to see if they are rumor, myth, wild speculation, impossible, or well-supported and likely true? Yes, you will. And you use the same kind of skills (different details, of course) to do both.
• Why is line b the height? It seems much smaller than line c. So how is it the height? -
• When Sal flipped the parallelogram so that b_ was the base, I found it helpful to flip the line _b that was on the triangle to the right of the parallelogram as well in my head. Since they are at a right angle to each other, it showed me that the hight of the parallelogram was in fact _b_.
• Who proved this theorem?
• The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it.
• At I don't understand how he found out that the height was b. What are the processes involved in finding the height. It just doesn't seem logical either.
• There is a version of side b that was rotated 90 degrees. It is used as the altitude of the parallelogram.
• Who created this proof? It is a lot like Bhaskara's proof.
• A person named Euclid made this proof. He was a Greek mathematician, who is often referred to as the "father of geometry
• I have another proof I made up. made a right triangle with sides a, b, and c and then attach three other sides to side c to make a square with each side that are size c. then you can sides that are size a and size b to each of the sides that are size c of the square. Once you do this for all sides that are c then you a square that each side being the size of a+b. then you can figure out the area of the large square and the smaller square and each of the 4 right triangles. so (a+b)^2 = 4(ab)/2 + c^2 =====> a^2+2ab+b^2 = 2ab + c^2 ===========> a^2 + b^2 = c^2
• What is the first known proof of the Pythagorean Theorem?
• Euclid first mentions it. I think in the beginning of High School Geometry, Sal mentions something about Euclid then.
• In the Pythagorean Theorem proofs exercises, there are some statements, "Triangle ABC and Triangle EFG are congruent by SAS". And, "The triangles are congruent by SSS". I've not come across the terms SAS and SSS before. Am I correct in guessing it's Side Angle Side, and Side Side Side?