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The Pythagorean theorem

You will learn about the importance of the Pythagorean Theorem in the video above.

Remember that, to implement the Pythagorean Theorem, a triangle has to be a right-angled triangle.

The longest side of a right-angled triangle is always opposite to the 90-degree angle (right angle). It is called the hypotenuse.

The other 2 adjacent sides are called the legs of the triangle.

Pythagorean theorem states that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other 2 sides.

1- Whatch the video "Pythagorean theorem explained" (here you have the transcription):

0:00 a squared plus b squared is equal to c squared is the pythagorean theorem

0:05 but where does the formula come from?

0:08 first we'll create a right triangle with sides a, b, and c

0:13 now if we were to place similar shapes on each side of the triangle

0:17 we will always get a remarkable relationship

0:22 the sum of the areas of the two smaller shapes

0:25 is always equal to the area of the larger shape

0:30 and there are many examples we can use and they all hold factually true

0:34 even with very unique shapes

0:39 so in order to show that the pythagorean theorem works

0:43 we will demonstrate it with squares

0:46 remember the area of a square is side squared

0:52 so from this we get a squared plus b squared

0:56 is equal to c squared

1:00 and by rearranging the shapes we can see that this is true

1:06 now the pythagorean theorem will always hold true as long as we always

1:10 maintain a right triangle

1:14 so there are many possible examples

1:17 and in every case we can always be able to arrange the shapes

1:21 to show that the pythagorean theorem

1:23 is true

1:28 now why does the pythagorean theorem work?

1:32 remember the angles of a triangle always add up to one hundred and eighty degrees

1:38 when we have a right triangle we have an angle that is always ninety

1:42 degrees

1:45 so the remaining two angles

1:47 must add up to ninety degrees

1:50 to have a total of a hundred and eighty degrees

1:55 therefore in every right triangle the sum of the two smaller angles is always

1:59 equal to the right angle

2:03 now in every shape the angle determines the length of the line

2:09 which in turn determines the size of the shape

2:13 so as we have seen before at the sum of the areas of the two smaller shapes is

2:17 equal to the area of the larger shape

2:20 which

2:21 is a direct result of the sum of the two smaller angles

2:25 equal to the right angle

2:29 so the pythagorean theorem works with any set of similar shapes

2:33 as long as we have a right triangle

2- Now watch the "Pythagorean theorem water demo", a very useful example which illustrate how the theorem works. Then, do the following tasks:

- Activity 1: use the sliders to explore the Pythagorean theorem (work in pairs)

- Activity 2: do the Hot Potatoes Match and check the solution (work individually, then discuss with your partner and finally check the solution)

- Activity 3: listen to the Pythagorean song. Try to identify the key words (at the end of the unit you have the lyrics but first listen without reading them).

- Activity 4: listen again to the Pythagorean Theorem explanation and then fill in the gaps. After that, compare your answers with your partner's and finally check your rights and wrongs (remember you have the transcription above but try to fill the gaps firstly without looking at it)

- Activity 5: solve the problems (write the septs down in your notebook, work in pairs).

- Activity 6: Play to the Pythagorean games (play two-on-two). You can also play alone whenever you want.

- Closure activity: Invent a problem in which you need to use the Pythagorean Theorem to get the solution. Include realistic mesures, units, etc.

PYTHAGOREAN SONG LYRICS

Look at a right triangle
With a 90 degree right angle
Across from the right angle is the hypotenuse
It's no surprise the hypotenuse is the longest side

Now how do you find the hypotenuse's length
If you know the length of the two other sides?
Let's take you back to ol' Ancient Greece
Pythagorus is gonna show you why:

a squared plus b squared equals c squared
Where c is the length of the hypotenuse
a squared plus b squared equals c squared
Where a and b are the length of the other sides

The Pythagorean Theorem
Is a delicate calculation
To find the hypotenuse take the square root
Of the sum of the two other sides' squares...and then compute

How do you find the hypotenuse's length
If you know the length of the two other sides?
Let's take you back to ol' Ancient Greece
Pythagorus is gonna show you why:

a squared plus b squared equals c squared
Where c is the length of the hypotenuse
a squared plus b squared equals c squared
Where a and b are the length of the other sides