2Tvwo §6.1 Pythagoras' theorem

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§6.1 Pythagoras' theorem

Before learning his so called famous theorem,

who the heck was Pythagoras?

Pythagoras

1. is made up, never lived
2. invented a formula about circles
3. was a famous Youtuber
4. was a Greek philosopher from the 6th century BC

In the next slide you...

+ what he could have looked like

+ even if he does not have the looks of a popstar

+ he still looks quite fresh in our 21st century's eyes!

    (except for the beard, perhaps...)

Task 1:

In pairs you get 6 paper SQUARES.

TASK 1: place  3    SQUARES with their vertices against each other, so that

the open space in the middle is a TRIANGLE !

Task 2:

Do the same with the other 3 SQUARES.

So connect them with their vertices.

Make a TRIANGLE in the middle, again!

Task 3: 

Study this picture.

QUESTION: What is the NAME

of the TRIANGLE in the middle?

ANS

The name of the triangle in the middle is ...

Task 3: 

SOLUTION:

it's a RIGHT-ANGLED

TRIANGLE!

Task 4: 

Make 2 RIGHT-ANGLED TRIANGLES

with the 6 SQUARES!

So select 2 groups of 3 SQUARES

first. Then see if you can produce

the desired result (=gewenste

resultaat).

ANS

Solution 4: 

You should have made 

two constructions like you see on the 

right!

All six squares are used to make

two right-angled triangles.

Pythagoras in a stamp.

Task 5:

Now that you have the two RIGHT-ANGLED TRIANGLES,

what is SURPRISING about the AREAS of the SQUARES?!

(The areas are written in the middle of the squares, in            .)

cm​2​​

Solution TASK 5:

The areas of the 2 smaller squares add up to the area of the greatest square!

WATCH THIS:

36 + 64 = 100   and also                       

144 + 256 = 400 !!

Some new words for a RIGHT-ANGLED TRIANGLE:

adjacent(=aangrenzend)  and  hypotenuse (=longest side)!

This square has two sides of 5 cm length.

What is the area of the square?

ANS 

The area is ....

1. 10
2. 20
3. 25
4. root 25

This square has two sides of 5 cm length.

What is the area of the square?

SOLUTION:

Area =  length x width = 5 x 5 = 25 

cm​2​​

Now the other way around:

The area of this square is  40.

What is size of the length and the width?

ANS

The length and width are ....

1. 10
2. 20
3. root 40
4. 5 and 8

SOLUTION:

The area of this square is  40.

What is size of the length and the width?

length = width = 

√​40​​​

Homework time. 

Do § 6.1      Skip exercise 3!

Make a good start yourself. Later this LessonUp is to be continued!

Pythagoras as a

thinker, I think.

Pythagoras' theorem.

Next slide shows you shortly what this is all about!

Let's do exercise 4 together now.

Make all steps in your Notebook!

Now we do a bit of the Homework together!

Write in your Notebook:

4 a.   Area smallest square = .............................

          Area smallest but one square  = .........................

    b.   Area square on hypothenuse = ..................................

    c.   c = ........ 

Solutions:

In the next slide you see ......

a very handy scheme, to calculate the unknown side!

Copy this scheme and fill it in!

Pay attention to this SCHEME right now.

It works wonders when dealing with Pythagoras exercises!

Use this scheme....

doing exercises 5, 6 now and later many others in this chapter!

Homework time.

Now that you know Pythagoras a bit more,

+      make a good use of his Theorem

+      applying this in the Scheme we made in exercise 4

+      good luck!