2Tvwo §6.1 Pythagoras' theorem

§6.1 Pythagoras' theorem
Before learning his so called famous theorem,
who the heck was Pythagoras?
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Slide 1: Tekstslide
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In deze les zitten 36 slides, met interactieve quizzen en tekstslides.

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§6.1 Pythagoras' theorem
Before learning his so called famous theorem,
who the heck was Pythagoras?

Slide 1 - Tekstslide

Pythagoras
A
is made up, never lived
B
invented a formula about circles
C
was a famous Youtuber
D
was a Greek philosopher from the 6th century BC

Slide 2 - Quizvraag

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...)

Slide 3 - Tekstslide

Slide 4 - Tekstslide

Slide 5 - Tekstslide

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 !

Slide 6 - Tekstslide

Task 2:
Do the same with the other 3 SQUARES.
So connect them with their vertices.
Make a TRIANGLE in the middle, again!

Slide 7 - Tekstslide

Task 3: 
Study this picture.
QUESTION: What is the NAME
of the TRIANGLE in the middle?
ANS

Slide 8 - Tekstslide

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

Slide 9 - Woordweb

Task 3: 
SOLUTION:
it's a RIGHT-ANGLED
TRIANGLE!

Slide 10 - Tekstslide

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

Slide 11 - Tekstslide

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.

Slide 12 - Tekstslide

Pythagoras in a stamp.

Slide 13 - Tekstslide

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            .)

cm2

Slide 14 - Tekstslide

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 !!

Slide 15 - Tekstslide

Slide 16 - Tekstslide

Some new words for a RIGHT-ANGLED TRIANGLE:
adjacent(=aangrenzend)  and  hypotenuse (=longest side)!

Slide 17 - Tekstslide

This square has two sides of 5 cm length.
What is the area of the square?
ANS 

Slide 18 - Tekstslide

The area is ....
A
10
B
20
C
25
D
root 25

Slide 19 - Quizvraag

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 
cm2

Slide 20 - Tekstslide

Now the other way around:
The area of this square is  40.
What is size of the length and the width?
ANS

Slide 21 - Tekstslide

The length and width are ....
A
10
B
20
C
root 40
D
5 and 8

Slide 22 - Quizvraag

SOLUTION:
The area of this square is  40.
What is size of the length and the width?
length = width = 
40

Slide 23 - Tekstslide

Homework time. 
Do § 6.1      Skip exercise 3!
Make a good start yourself. Later this LessonUp is to be continued!

timer
5:00

Slide 24 - Tekstslide

Pythagoras as a
thinker, I think.

Slide 25 - Tekstslide

Pythagoras' theorem.
Next slide shows you shortly what this is all about!

Slide 26 - Tekstslide

Slide 27 - Tekstslide

Slide 28 - Tekstslide

Let's do exercise 4 together now.
Make all steps in your Notebook!

Slide 29 - Tekstslide

Slide 30 - Tekstslide

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 = ........ 
timer
1:30

Slide 31 - Tekstslide

Solutions:

Slide 32 - Tekstslide

In the next slide you see ......
a very handy scheme, to calculate the unknown side!
Copy this scheme and fill it in!

Slide 33 - Tekstslide


Pay attention to this SCHEME right now.
It works wonders when dealing with Pythagoras exercises!

Slide 34 - Tekstslide

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

Slide 35 - Tekstslide

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! 

Slide 36 - Tekstslide