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Goal: Find the side lengths of triangles using the Pythagorean Theorem.
Pythagorean What?
A theorem is a math rule. The Pythagorean Theorem is a rule that is used to find the lengths of the sides of right triangles. It's on page 413 of your book, but here it is again just for reference:
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This is not as bad as it sounds, honest. In order to understand this you have to know some of the vocabulary.
First you have to know what a right triangle is. The Pythagorean Theorem pertains ONLY to RIGHT TRIANGLES. A right triangle is a triangle with one angle measuring exactly 90 degrees.
Next you need to know what a hypoteneuse is. Hypoteneuse is just a fancy word for the longest side of a right triangle. It is ALWAYS the side ACROSS FROM the right angle.
Finally, you have to know what the legs are. The legs are the sides of the triangle that come together to make the right angle. Or, you could think of the legs as the other two sides besides the hypoteneuse.
There is a diagram of this at the bottom of page 412. Here's another one, just for reference.
NOTICE that the HYPOTENEUSE is labeled with a LOWERCASE c. This is the way it's usually done.
Finding the Length of a Leg
Now, the mathmatical formula for the Pythagorean Theorem is:
How the heck are we going to use that? Well, let's say you have a triangle like this one:
You need to find out the length of side a. How?
Remember that I said the hypoteneuse is represented by c and the legs by a and b? Well, that means you can plug in those numbers into the formula. If you do that, you get something that looks like this:
Okay, so far so good. Now you can at least calculate the squares of the numbers you have. You know, 7 x 7 and 17 x 17.
Good, now who can tell me how to figure out what a is?? Anyone? Don't all jump up at the same time.
Remember? You have to get the a by itself on one side of the = sign. To do this you must move the 49 over, and anytime you move one number to the other side of an = sign, you change to the opposite sign. SO.......
Now all you have to do is figure the rest out. Hmm, what times what = 240? How on earth could you figure that out???
Hello, square root key! The square root of 240 is 15.5. Therefore,
Finding the Length of the Hypoteneuse
The good news is, it's even easier than finding the length of the leg. The only difference between this and the problem we just did is that you don't have to move anything or change any signs. Just square the lengths of the legs, add them together, and find the square root of the answer. That number will be the length of the hypoteneuse.
You try it:
This one is a challenge, but you CAN do it.
Suppose I drew a bunch of triangles, but I forgot to make the little "right angle" symbol on some of them. I'm a really bad artist, so most of the triangles look like right angles, but I know not all of them are. Can you figure out which of these is a right triangle? (There may be more than one!)
HINT: Use the Pythagorean Theorem. Plug in the numbers. Which one(s) fit(s)?
No peeking! You can do it!