# 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.

Lesduur 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 3 -Tekstslide

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

A plane is a
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 11 -Tekstslide

Verlengde stelling van Pythagoras:

#### 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 16 -Tekstslide

Pythagoras was good in Solids too!

#### Slide 17 -Tekstslide

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

#### Slide 19 -Tekstslide

Solids: how to describe them

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 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 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),
Remember that it's all about looking for right-angled-triangles and the
making SKETCHES and SCHEMES to CALCULATE the missing lengths!!

#### Slide 32 -Tekstslide

Question: What was that animal?