2Tvwo § 4.5 Mixed exercises

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 2

§ 4.5 Mixed exercises   today!

First let's look back at a difficult exercises from

§ 4.4:   exercise 30, page 140.

Open your Textbook!

Open your Notebook, too.

MAKE 30a now!

Answer to 30a What is the factor to multiply the sides of PQRS by to get KLMN, is ..........

1. root 9
2. 3
3. 9
4. 1/3

Do you remember from §4.4 ?

When discussing two SIMILAR figures, then

- the dimensions are multiplied by, say k

- the perimeter is also multiplied by k, however

- the AREA is multiplied by 

k​2​​

30 a The solution:

1st we calculate the factor by which to multiply area PQRS by to get area KLMN.

That is 144 : 16 = 9

2nd We know that we have to take the ROOT of 9, to get the SCALE FACTOR from PQRS to KLMN

So: Root 9 = 3 = Scale Factor!

Now MAKE 30b in your Notebook!

Remember that is was a Homework task for today!

30b The solution:

Let's keep it as simple as can be.

(The Solutionsbook, normally very good, gives a pretty difficult solution...)

We make a table for the possibilities of the squares. 

We start with the area of 16 squared cm, because that has very few possibilities. Only 3, see next slide!

All possibilities follow here:

                            PQRS:                        KLMN:

1st:              1 cm x 16 cm         3 cm x 48 cm

2nd:            2 cm x 8 cm          6 cm x 24 cm

3rd:             4 cm x 4 cm          12 cm x 12 cm                            

Now a few questions about § 4.5,

today's homework.

Question about 31, page 142:
What Method is needed here?

1. Finding all squares from numbers 1 to 9.
2. Checking angles and sides too.
3. Checking if the angles are equal.
4. Checking the sides.

I want you to be COMPLETE in 31a:

1. calculate the unknown angles 

2. make pairs of equal angles

3. make a ratio table for finding a ratio table (if there is one!)

4. conclusion: are the quadrilaterals similar or not?

Read 32a carefully.
NOTE: we start from the real Dutch parts and
end at the models in Madurodam.
What is the best answer to it?

1. 1/25
2. 0.04
3. 25
4. 1:25

Many exercises ask you to calculate the lengths of sides.
What is the best method for this?

1. Calculator.
2. Make a ratio table.
3. Hugging your neighbour.
4. Comparing the angles.

Mistake in 36!

Correct the following mistake, but only with a PENCIL!!

'In rectangle ABCD, triangle ABD is an enlargement of triangle ADE.'

In this sentence, the triangles should be exchanged.

Change this in a neat way, only with a pencil.

Now do § 4.5!