2Tvwo §6.4 Pythagoras in solids

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 3

§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

a partition is a ......

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

A plane is a

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

Finally...

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!!

and B. Slant roofs on a house.

Watch next slide!

Pythagoras was good in Solids too!

He was a solid man. Our hero. What a guy...

His theorem....

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

TASK:

Find out which side you have to calculate in these 3 solids.

The answer is in the next slide.

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

HOW can you calculate AC ?   As follows:

+  drawing the CROSS-SECTION

+  writing down all measurements and

+  making the SCHEME of Pythagora

Homework time.

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

Skip 25, 30

It's Pyramid time!

How come?

Exercises 28, 29 and 30 happen to about these massive buildings.   

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.

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 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 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 dutch:  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

Work hard on this and soon you will become a real PP

(=Pythagoras Pro).