# 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: Slide
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This lesson contains 36 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

## Items in this lesson

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

#### Slide 1 -Slide

Pythagoras
A
B
C
D
was a Greek philosopher from the 6th century BC

#### Slide 2 -Quiz

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 5 -Slide

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 -Slide

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

#### Slide 7 -Slide

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

#### Slide 8 -Slide

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

#### Slide 9 -Mind map

SOLUTION:
it's a RIGHT-ANGLED
TRIANGLE!

#### Slide 10 -Slide

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 -Slide

Solution 4:
two constructions like you see on the
right!
All six squares are used to make
two right-angled triangles.

#### Slide 12 -Slide

Pythagoras in a stamp.

#### Slide 13 -Slide

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 -Slide

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 16 -Slide

Some new words for a RIGHT-ANGLED TRIANGLE:

#### Slide 17 -Slide

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

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

#### Slide 19 -Quiz

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 -Slide

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

#### Slide 21 -Slide

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

#### Slide 22 -Quiz

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

#### Slide 23 -Slide

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 -Slide

Pythagoras as a
thinker, I think.

#### Slide 25 -Slide

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

#### Slide 28 -Slide

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

#### Slide 30 -Slide

Now we do a bit of the Homework together!
4 a.   Area smallest square = .............................
Area smallest but one square  = .........................
b.   Area square on hypothenuse = ..................................
c.   c = ........
timer
1:30

Solutions:

#### Slide 32 -Slide

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

#### Slide 33 -Slide

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

#### Slide 34 -Slide

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

#### Slide 35 -Slide

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!