An Introduction to the Pythagorean Theorem | Math with Mr. J

Welcome to Math with Mr. J.

In this video, I'm going to go through an introduction to the Pythagorean Theorem.

Now, the Pythagorean Theorem has to do with right triangles and the relationship

between the sides of right triangles. It's called the Pythagorean Theorem because

it's named after Pythagoras, a greek philosopher and mathematician. Let's jump into

our examples and see exactly what this all means and looks like, starting with number

one, where we have a right triangle. Now remember, the Pythagorean Theorem applies

to only right triangles. Before we get started with the specifics of the Pythagorean

Theorem, we need to take a look at the sides of this triangle and we are going to start with this side right here,

the side directly across from the right angle. This is called the

hypotenuse.

The hypotenuse is the longest side of a right triangle. And again, it will be across

from, or opposite of, the right angle. This is something we need to recognize and

know when it comes to the Pythagorean Theorem. Then we have the other two shorter

sides. So this side right here and this side right here. These are called the legs.

So this is a leg and this is a leg. The Pythagorean Theorem states that the sum of

the legs squared will equal the hypotenuse squared. So the length of the legs squared,

add those together, and that will equal the hypotenuse squared. And that probably

sounds confusing worded like that, so let's write it out as an equation, a squared

plus b squared equals c squared. So for the Pythagorean Theorem, we use that equation.

Again, a squared plus b squared equals c squared. Now a, b, and c all represent a

side of the triangle. Let's start with c. Now c is always going to be the hypotenuse.

So let's put a c here. And then a and b are going to be the legs. It does not matter

which leg is a and which is b. It will work out the same the same either way. So let's call this

a and this b. So what we are going to do, we are going to use the pythagorean theorem,

the equation a squared plus b squared equals c squared, to figure out the missing

side length, this side right here, the hypotenuse. If we know two of the side lengths,

we can use the Pythagorean Theorem to figure out the missing side length. Let's plug

in the information we know in order to figure out the information we don't know.

So we have both of the legs given, a and b, so let's plug those into the equation. So a squared

plus b squared

equals c squared. Again, we are given a and b, so let's plug those in. a is four feet,

so four feet squared. Plus b is 3 feet, so 3 feet squared.

Equals c squared. Now we can work through this equation and solve for c, so we need

to figure out what c equals. Let's start with the left side of the equation. So 4

squared plus 3 squared. 4 squared means 4 times 4, so that gives us.

16. Plus 3 squared, that means 3 times 3. That gives us 9. Equals c squared. 16 plus

9, that equals 25 equals c squared. Now we need to isolate that variable of c and

get rid of the exponent of 2. We do that by taking the square root. So let's take