2Tvwo §6.5 Right, acute or obtuse

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§6.3 Right, acute or obtuse ?

Before going over to §6.5...

Let's Study the last exercise from §6.4!

Open your notebook,

+ Watch your Homework and 

+ Check if you have exercise 30

If you do have 30, then

be proud and   stand up!

exercise 30

What makes this exercise difficult, is...

that you do not have a 3D picture of the pyramid!

This makes it hard to imagine what all the information in words means.

'Use cross-section LTN .......'  - What's all that??!

Question:

What could you do first, to solve this problem?

(How to have a good overview on all information?)

Answer to the question:

Answer:

Make my own 3D sketch of the pyramid!

Here is my sketch.

Indeed, a true

work of Art!

Once more the exercise and the 3D pic:

Now only we sketch cross-section LTN !

Then we take a few steps:

1st  In LTN we draw a help-line: TX. This is the height we have to calculate.

2nd  We calculate LN  (in order to know NX !).

3rd  We calculate NX.

4th We calculate height TX !    

§6.5 at last...

Some new words:

+  converse (The converse Pythagoras' theorem; in between 31 and 32)

      = opposite (omgekeerde)

+  Two slats of wood are fixed together by a hinge. (33)

      hinge =  scharnier

Let's do this task together 

Write the solutions in your Notebook!

It is an important 

exercise to understand this paragraph.

Solution:

Copy the SCHEME, fill it in

and calculate BC.

Solution:

Also EXPLAIN why (not)!

Solution:

Solution:

This is what we've learnt now: 

Homework time.

Make a good start with §6.5 yourself!

Later on a few more slides follow.

 

Question: If the text below is the 'converse Pythagoras' Theorem, then what is the 'original one'?!  Answer on next slide.

Answer: the original theorem you see below (p.201).

The point is that here we START with a right-angled triangle!

In the converse one we draw the CONCLUSION that the triangle is right-angled!

Question about 32b:

how to know which side is the longest, 24 or                   ?

(Important, because that one has to below, in the Scheme!)

√​600​​​

​[?]​​√​600​​​

How to find which is greatest:
or 24 ?!

Answer for 32b:

Key in                              on your calculator:

is about 24.49,   so

LM =                     is the longest,

because KL = 24 and KM = 2.

√​600​​​

√​600​​​

√​600​​​

Tip for 33:

This exercise is a GREAT INTRODUCTION + EXPLANATION

for the rest of the whole paragraph!

Make sure you understand this one, before you go on!

Homework time again!