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Wiskunde
Middelbare school
vwo
Leerjaar 3
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Slide 1 - Diapositive
6.4 Pythagoras in solids
First we look at some new words:
+ partition + cross-section
+ plane + intermediate results
+ wire model + slant edges
Slide 2 - Diapositive
a partition is a ......
(ex. 24a)
A
sweet cake
B
divider
C
a special type of fraction
D
request
Slide 3 - Quiz
Ex.24
Slide 4 - Diapositive
A plane is a ...
(ex.25)
A
flat surface
B
aeroplane
C
thought
D
development
Slide 5 - Quiz
These are 'planes', 'partitions' or 'cross-sections'.
There is not much difference between the meaning of these words.
Slide 6 - Diapositive
What is a wire model?
A
a catwalker
B
a model wearing iron clothes
C
3D model with only vertices and lines
D
a light car, made of wire only
Slide 7 - Quiz
A wireframe is a three-dimensional
model that only includes
vertices and lines.
It does not contain
surfaces or textures.
Slide 8 - Diapositive
Important, remember!
An intermediate result:
for example the answer from question a),
that you need again at question b) - and therefore should not yet be rounded!!!!
Slide 9 - Diapositive
Slant roofs on a house.
Watch next slide!
Slide 10 - Diapositive
Slide 11 - Diapositive
Pythagoras was good in Solids too!
Slide 12 - Diapositive
His theorem....
is also used to calculate lengths in cubes, cuboids etc.
Slide 13 - Diapositive
Homework time.
Discover Pythagoras in 3D yourself, today! Later this LessonUp is continued.
Slide 14 - Diapositive
Slide 15 - Diapositive
That was short, wasn't it?
It's Homework time again
Later we will have a look at (calculations in) pyramids.
Slide 16 - Diapositive
Slide 17 - Diapositive
ex. 28, 29 and 30 are about pyramids!
To CALCULATE the HEIGHT it is important to
+ make good SKETCHES and
+ make the corresponding SCHEMES again!
+ Let's have a short look at ex. 28.
Slide 18 - Diapositive
Slide 19 - Diapositive
Slide 20 - Diapositive
28a The sketch of TPR:
This is all fine, but we cannot calculate
height TQ yet!
We do not know TQ nor RT.
That's why......
Slide 21 - Diapositive
We will use face BCT.
Why?
+ to first calculate RT an only then
+ calculate TQ!
+ Of BCT we happen to know:
+ BT = 6 and BR = 2
+ For a SKETCH, see next slide!
Slide 22 - Diapositive
This was just an
INTRODUCTION to
28 (29 and 30),
about Pyramids.
Remember that it all about looking for right-angled-triangles and the
making SKETCHES and SCHEMES to CALCULATE the missing lengths!!
Slide 23 - Diapositive
Slide 24 - Diapositive
Question: What was that animal?
Answer: a HIPPOPOTAMUS,
or in good German: een nijlpaard.
The joke is that this word is a bit similar to
HYPOTENUSE (longest side of a right-angled triangle).
Slide 25 - Diapositive
Homework time again.
Good luck, making §6.4
Soon you will become a real Pythagoras Pro!
Slide 26 - Diapositive
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