Getting started

Hi, my name is alexia Gilbert.

And today I'll be taking you through the

pythagorean theorem and the pythagorean theorem converse.

So let's get started

first of all. What is the pythagorean theorem and converse?

Well,

both the Pythagorean theorem and the pythagorean theorem converse expresses

the connections between all three sides of a right triangle.

With this concept, the two shortest sides, legs are known as A. And B.

And the longest side furthest from the right angle C.

Is called the hypotenuse.

The pythagorean theorem helps us find the value of C. A. K. A.

The hypotenuse by squaring the A. And B.

Values and finding the square root of that sum.

On the other hand, the pythagorean theorem converse gives us gives us the A. B and C.

Values and leaves it up to us to determine whether or not a figure is a right triangle.

The formula and foundation.

When looking at the pythagorean theorem, our goal is to find the value of C.

We can do this by using the formula A squared plus B squared equals C squared.

You basically have to multiply each leg value by itself

in order to find the value of the hypotenuse,

let's practice

let's start with this problem.

Starting with problem number one, we can see that A measures six inches

to square this value. You'd multiply six by six to get 36.

The same thing goes for B, which measures 8".

This will give you a product of 64.

Now you must add those two numbers together and what do you get 100.

But wait,

you're not quite done yet because this is the squared value not the original

from here, it's pretty simple to find your true answer.

That is if you know a thing or two about square roots

to clarify A square root is a number that

when multiplied by itself gives you a certain answer

Example would be five times five equals 25. So the square

Route five is 5,

You can do the same thing here.

If you've been studying your multiplication facts,

you know that 10 times 10 gives you a product of 100

This means that 10,

the square root of 100 is the actual answer.

To summarize this.

The equation should look like six squared plus a squared equals 10 squared

with 10 squared being the actual answer.

Now onto the Pythagorean theorem, converse,

what is the pythagorean theorem converse

in this theorem will use the same concept as the Pythagorean theorem,

but in a slightly different way.

Instead of solving for the value of C will be using the A B,

A B and C values to determine whether or not a figure is a right triangle.

We're going to use the converse statement,

If a squared plus b squared equals c squared,

then the triangle is a right triangle. For problem number one

in this problem A equals 11 ft, B equals 13 ft, and c equals 16 ft

for the squared values 11 times 11 equals 121 13

times 13 equals 169 and 16 times 16 equals 256

Now that we know what our official values are, we know what we're aiming for.

256.

So when you add 121 and 169 together you get 290, not 256.

So in this state, so the statement, if a squared plus B squared equals C squared,

then the triangle is a right triangle doesn't apply here.

Let's try a different problem

and see if we get the same result

for this one,

A equals six ft, b equals eight ft, and c equals 10 ft.

When we square these values we get 36,

and 100.

And when you add 36 plus 64 together

you get 100.

So in this case the statement, if a squared plus B squared equals c squared,

then the triangle is a right triangle

does apply here.

Let's review what we've learned.

Right triangles have three parts to them,

the legs which are the shorter sides closest to the right angle

and the hypotenuse which is the longest side furthest from the right angle.

They're also known as A

B

and C.

The pythagorean theorem expresses the relationships

between the legs and hypotenuse and

it states that when the A and B values are squared,

they should equal to the squared see value.

Then the pythagorean theorem converse helps us

determine the status of the triangle,

whether a right triangle or not.

This test our knowledge and lets us use the converse statement to see for ourselves.

One of the ones we can really apply is the original statement.

If a triangle is a right triangle, then a squared

plus b squared equals c squared,

and the converse statement, if a squared plus b squared equals c squared,

then the triangle is a right triangle.

I hope you gained a lot from this lesson, and I hope to see you soon.

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