Pythagorean Theorem

Pythagorean Theorem

Thursday Dec 17, 2020

Poll

Warm - up: When you hear "Pythagorean Theorem" does that sound like something you've heard before, or is it brand new?

• Brand new

• I've maybe heard it before?

• I've heard it, I know it, I could tell you all about it right now

• I've definitely heard it before

Pythagorean Theorem

Pie-thag-or-ian Thee-or-um

It's named after Pythagoras Of Samos, if you've never heard of him you should look him up sometime, he was a pretty cool dude.

Okay okay, enough History, let's get to it

But seriously, though, Google him sometime... :)

The Pythagorean Theorem

can only be used with right triangles, but even so it comes up a surprising amount. And it works every time, so that's cool.

a² + b² = c²

"the sum of the squares of the legs is equal to the square of the hypotenuse"

...What?

a² + b² = c²

a and b are interchangeable, meaning they can go in either spot. But c is ALWAYS the hypotenuse

To solve for c

• a = 3, b = 4

• a² + b² --> 3² + 4²

• 3² = 9, 4² = 16

• 9 + 16 = 25

• 25 = c²

• 
  
   $\sqrt{25}=\sqrt{c^2}$  
  

• 5 = c

But... what happens if c isn't a perfect square?

*A perfect square is a number that when you square root 

( $\sqrt{x}$  ) it, you get a whole number

 $\sqrt{9}=3$     9 is a perfect square

  $\sqrt{5}\approx\ 2.236...$      5 is not a perfect square

Let's say...

• a = 2, b = 3

• 2² + 3² = c²

• 4 + 9 = c²

• 13 = c²

• 
  
   $\sqrt{13}=c$  
  

• That is a perfectly acceptable answer, don't make it some rounded decimal. Just leave it alone 

Go practice

Google Classroom has your assignment