2Tvwo §6.2 Calculating a side

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• Leerjaar 2

§6.2 Calculating a side

Do you remember our old, bearded friend from the past?

Who is he?

Solution:

Welcome back to: Pythagoras!

Lived from 570 - 500 before Christ.

Previous slide showed us another picture

of this great Maths chap.

Not just a next door guy, isn't he?

 .

The theorem of Pythagoras

1. is about the sides of a right-angled triangle
2. is used to calculate an unknown angle
3. is invented by Pete Agoras
4. is more than 2500 years old but still going strong

The theorem of Pythagoras...

asks for the use of a very handy scheme!

TASK:  +  Make the SKETCH for 8a,

              +  Take a picture and 

              +  Send it in in GC

              +  This is a FOTOVRAAG!        

Let's do exercise 8 together,

start doing 8 a), in your Notebook.

MAKE A SKETCH for 8a, and SEND IT IN BY A FOTOVRAAG! (next slide)

Sketch triangle KLM with angle K = 90 degrees and
KL = 15 and LM = 20
Take a pic and send it in here!

Here is the sketch:

Of course this triangle could 

also be made upside down.

As long as angle K is 90 degrees!

Now think hard about b:

answer for b:

Do c now:

First copy the scheme! Then:

answer for c:

Watch Pythagoras, going crazy about his own Theorem!

Where?

Next slide!

Time to do d:

Do this task in your scheme from c!

Think about the meaning of the words: 'exact length'.

answer for d:

'exact' means: not rounded off! 

So write it as a ROOT.

Next slide gives you an important TIP!

A TIP for doing 9:

For 9a, b and c you are asked to calculate an unknown side.

USE THE METHOD SHOWN ABOVE EXERCISE.

Watch the next slide!

This handy SCHEME you just used for doing exercise 8.

When doing the FOLLOWING TASKS (9  t/m  15)

make a good use of this EVERY TIME!

Homework time.

Do §6.2 now, 

+  start with 7, then 9, 10, etcetera

+  make the SCHEME with lengths for every exercise!!

+  remember to place the hypotenuse (=longest side) at the bottom

+ later on this LessonUp is continued

A few fine points from this paragraph follow now!

We want to calculate length BD.

What to calculate FIRST?

Give your answer in the next slide.

We want to calculate BD.
What to calculate first?

Solution:   First calculate length CD in right-angled triangle ACD.

Then only calculate length BD in right-angled triangle BCD!

How (on earth) can you calculate DE or GH?

We do not even have a right-angled triangle! 

(see next slide)

Solution: we make a right-angled triangle ourself!!

With that we can make the SCHEME and calculate the unknown side.

Question: Think of a Method to do the exercise, below!

The best Method might be:

Making a SKETCH!

How else can we see what to calculate?!

See next slide!

How to go on?

For every line segment you can now make a 

Pythagoras scheme. 

All lengths will become known.

 Then you can compare them, to find the greatest and the smallest.

Homework time again.

Finish as much as you can!