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

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• Leerjaar 3

§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!

Dagopening?

Gebed

Bijbel

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

a partition is a ......

1. sweet cake
2. divider
3. a special type of fraction
4. request

A plane is a
(3 answers!)

1. flat surface
2. aeroplane
3. thought
4. development

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)

What is a wire model?

1. a catwalker
2. a model wearing iron clothes
3. 3D model with only vertices and lines
4. a light car, made of wire only

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

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!)

Berekenen lichaamsdiagonaal

> met een tussenstap ( via lichaamsvlak)

> Verlengde stelling van Pyth:

 https://www.youtube.com/watch?v=nx0Foklfkdk

Verlengde stelling van Pythagoras:

video (Wiskunde academie)

Time to do (and check!!!) HW

Make of 6.4: 24, 26 and 27.

6.4 part 2 Pythagoras in solids

Pythagoras was good in Solids too!

His theorem....

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

Solids: how to describe them

video uitrekenen lengte lichaamsdiagonaal (Moderne Wiskunde)

Homework time.

That was short, wasn't it?

It's Homework time again

Later we will have a look at (calculations in) pyramids.

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.

Video height in pyramid

start min 8.43

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......

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!

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!!

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).

Homework time again.

Good luck, making your HW

Soon you will become a real Pythagoras Pro!