6.4 Pythagoras in solids part 1_2vtto

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• Leerjaar 3

6.4 Pythagoras in solids

First we look at some new words:

+ partition                                                                   + cross-section

              + plane                                                                                   + intermediate results

+ wire model                                                                                    + slant edges

a partition is a ......

(ex. 24a)

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

Ex.24

A plane is a ...

(ex.25)

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.

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 or textures. 

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!!!!

Slant roofs on a house.

Watch next slide!

Pythagoras was good in Solids too!

His theorem....

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

Homework time.

Discover Pythagoras in 3D yourself, today! Later this LessonUp is continued.

That was short, wasn't it?

It's Homework time again

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

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.

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 an 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 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 §6.4

Soon you will become a real Pythagoras Pro!