# 2Tvwo §6.4 Pythagoras in solids

§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
1 / 34
Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 3

In deze les zitten 34 slides, met interactieve quizzen en tekstslides. Lesduur is: 50 min

## Onderdelen in deze les

§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

#### Slide 1 -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 6 -Quizvraag

These are 'planes', 'partitions' or 'cross-sections'.
There is not much difference between the meaning of these words.

#### Slide 7 -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 9 -Tekstslide

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!!

#### Slide 10 -Tekstslide

and B. Slant roofs on a house.
Watch next slide!

#### Slide 13 -Tekstslide

Pythagoras was good in Solids too!
He was a solid man. Our hero. What a guy...

#### Slide 14 -Tekstslide

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

#### Slide 15 -Tekstslide

Find out which side you have to calculate in these 3 solids.
The answer is in the next slide.

#### Slide 16 -Tekstslide

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

#### Slide 17 -Tekstslide

HOW can you calculate AC ?   As follows:
+  drawing the CROSS-SECTION
+  writing down all measurements and
+  making the SCHEME of Pythagora

#### Slide 19 -Tekstslide

Homework time.
Discover Pythagoras in 3D yourself, today! Later this LessonUp is continued.
Skip 25, 30

#### Slide 24 -Tekstslide

It's Pyramid time!
How come?
Exercises 28, 29 and 30 happen to about these massive buildings.

#### Slide 25 -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 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 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 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?