2TTO §6.4 Pythagoras in solids 21-22 vanaf slide 23 PTI

§6.4 Pythagoras in solids
Learning goal: how to calculate the length of a line segment in a solid

First we look at some new words:
+ partition                                                                   + cross-section
              + plane                                                                                   + intermediate results
+ wire model                                                                                    + slant edges (S29)


Moderne Wiskunde site -> video!
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Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 3

In deze les zitten 35 slides, met interactieve quizzen en tekstslides.

time-iconLesduur is: 50 min

Onderdelen in deze les

§6.4 Pythagoras in solids
Learning goal: how to calculate the length of a line segment in a solid

First we look at some new words:
+ partition                                                                   + cross-section
              + plane                                                                                   + intermediate results
+ wire model                                                                                    + slant edges (S29)


Moderne Wiskunde site -> video!

Slide 1 - Tekstslide

Dagopening?
Gebed
Bijbel
Lauren Daigle,  rolling stones -> https://www.youtube.com/watch?v=a2zeEQq0bKo

Slide 2 - Tekstslide

Slide 3 - Tekstslide

a partition is a ......
A
sweet cake
B
divider
C
a special type of fraction
D
request

Slide 4 - Quizvraag

A plane is a
(3 answers!)
A
flat surface
B
aeroplane
C
thought
D
development

Slide 5 - Quizvraag

These are 'planes', 'partitions' or 'cross-sections'. 
There is not much difference between the meaning of these words.
A
Cuboid ABCD.EFGH
Je begint linksbeneden, tegen klok in. Eerst die 4 beneden, dan PUNT en dan bovenkant (linksboven beginnen, zelfde volgorde)

Slide 6 - Tekstslide

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 - Quizvraag

A wireframe is a three-dimensional model that only includes vertices and lines. It does not contain surfaces.

Slide 8 - Tekstslide

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

Een tussengetal rond je niet tussendoor af!
Gewoon doorrekenen met dat getal (ook als het een Wortel is!)

Slide 9 - Tekstslide

Berekenen lichaamsdiagonaal

> met een tussenstap ( via lichaamsvlak)

Slide 10 - Tekstslide

Slide 11 - Tekstslide

Verlengde stelling van Pythagoras:


video (Wiskunde academie)


Slide 12 - Tekstslide

Time to do (and check!!!) HW
Make of 6.4: 24, 26 and 27.

Slide 13 - Tekstslide

6.4 part 2 Pythagoras in solids

Slide 14 - Tekstslide

Slide 15 - Tekstslide

Slide 16 - Tekstslide

Pythagoras was good in Solids too!

Slide 17 - Tekstslide

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

Slide 18 - Tekstslide

Slide 19 - Tekstslide

Solids: how to describe them

Slide 20 - Tekstslide

Homework time.

Slide 21 - Tekstslide

That was short, wasn't it?
It's Homework time again
Later we will have a look at (calculations in) pyramids.

Slide 22 - Tekstslide

Slide 23 - 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 24 - Tekstslide

Video height in pyramid
start min 8.43

Slide 25 - Tekstslide

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.
Why?
+ to first 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
INTRODUCTION to
28 (29 and 30),
about Pyramids.
Remember that it's 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?
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 33 - Tekstslide

Homework time again.
Good luck, making your HW
Soon you will become a real Pythagoras Pro!

Slide 34 - Tekstslide

Slide 35 - Tekstslide