2Tvwo §6.4 Pythagoras in solids

§6.4 Pythagoras in solids (not 25, 30)
First we look at some new words:
+ partition                                                                   + cross-section
              + plane                                                                                   + intermediate results
+ wire model                                                                                    + slant edges
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Slide 1: Tekstslide
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In deze les zitten 34 slides, met interactieve quizzen en tekstslides.

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§6.4 Pythagoras in solids (not 25, 30)
First we look at some new words:
+ partition                                                                   + cross-section
              + plane                                                                                   + intermediate results
+ wire model                                                                                    + slant edges

Slide 1 - Tekstslide

a partition is a ......
sweet cake
a special type of fraction

Slide 2 - Quizvraag

Slide 3 - Tekstslide

Slide 4 - Tekstslide

Slide 5 - Tekstslide

A plane is a
flat surface

Slide 6 - Quizvraag

These are 'planes', 'partitions' or 'cross-sections'. 
There is not much difference between the meaning of these words.

Slide 7 - Tekstslide

What is a wire model?
a catwalker
a model wearing iron clothes
3D model with only vertices and lines
a light car, made of wire only

Slide 8 - Quizvraag

Slide 9 - Tekstslide

A.   An intermediate result:
for example the answer from question a), that you need again at question b) - and therefor should not yet be rounded!!

Slide 10 - Tekstslide

and B. Slant roofs on a house.
Watch next slide!

Slide 11 - Tekstslide

Slide 12 - Tekstslide

Slide 13 - Tekstslide

Pythagoras was good in Solids too!
He was a solid man. Our hero. What a guy...

Slide 14 - Tekstslide

His theorem....
is also used to calculate lengths in cubes, cuboids etc.

Slide 15 - Tekstslide

Find out which side you have to calculate in these 3 solids.
The answer is in the next slide.

Slide 16 - Tekstslide

Solution           what's to be calculated is the following:
- There's only the skew (or slanted) edge from every rectangle,
   because the other sides are given
- So: AC,  BG and BE have to be calculated only

Slide 17 - Tekstslide

HOW can you calculate AC ?   As follows:
+  drawing the CROSS-SECTION
+  writing down all measurements and
+  making the SCHEME of Pythagora

Slide 18 - Tekstslide

Slide 19 - Tekstslide

Homework time.
Discover Pythagoras in 3D yourself, today! Later this LessonUp is continued.
Skip 25, 30

Slide 20 - Tekstslide

Slide 21 - Tekstslide

Slide 22 - Tekstslide

Slide 23 - Tekstslide

Slide 24 - Tekstslide

It's Pyramid time!
How come?
Exercises 28, 29 and 30 happen to about these massive buildings.   

Slide 25 - Tekstslide

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 28.

Slide 26 - Tekstslide

Slide 27 - Tekstslide

Slide 28 - Tekstslide

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 29 - Tekstslide

We will use face BCT.
+ to calculate RT and only then
+ calculate TQ!
+ Of BCT we happen to know:
+ BT = 6  and BR = 2 
+ For a SKETCH, see next slide!

Slide 30 - Tekstslide

This was just an
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 31 - Tekstslide

Slide 32 - Tekstslide

Question: What was that animal?
or in dutch:  een nijlpaard.
The joke is that this word is a bit similar to 
HYPOTENUSE (longest side of a right-angled triangle).

Slide 33 - Tekstslide

Homework time again.
Good luck, making §6.4
Work hard on this and soon you will become a real PP
(=Pythagoras Pro).  

Slide 34 - Tekstslide