Which exercises/theories should we discuss on the board?
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Slide 1: Woordweb
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2
In deze les zitten 20 slides, met interactieve quiz en tekstslides.
Lesduur is: 50 min
Onderdelen in deze les
Which exercises/theories should we discuss on the board?
Slide 1 - Woordweb
Shorter sides & hypotenus
All right-angled triangles have 2 shorter sides and 1 hypotenuse.
The hypotenuse is the longest side and always lies opposite the right angle.
The shorter sides are (as the name suggests)
shorter than the hypotenus and always lie
on either side of the right angle.
Slide 2 - Tekstslide
Exercise 2
2a) Which sides are the shorter sides
of triangle ABC?
Slide 3 - Tekstslide
Exercise 2
2a) Which sides are the shorter sides
of triangle ABC?
AB and AC
Slide 4 - Tekstslide
Exercise 2
2b) Calculate the area of square
ACHI and the area of square ADEB
Slide 5 - Tekstslide
Exercise 2
2b) Calculate the area of square
ACHI and the area of square ADEB
area ACHI = 3 x 3 = 9
area ADEB = 4 x 4 = 16
Slide 6 - Tekstslide
Exercise 2
2c) Calculate the area of square
BFGC by enclosing the square
Slide 7 - Tekstslide
Exercise 2
2c) Calculate the area of square
BFGC by enclosing the square
Area BFGC = 25
Slide 8 - Tekstslide
Exercise 2
2d) Add the areas of square ACHI
and square ADEB together.
What do you notice?
Slide 9 - Tekstslide
Exercise 2
2d) Add the areas of square ACHI
and square ADEB together.
What do you notice?
9 + 16 = 25.
This is the same as the area of BFGC
Slide 10 - Tekstslide
Exercise 2
2e) Calculate the lenght of BC
Area of the square is 25, so the
lenght of BC =
Slide 11 - Tekstslide
Pythagoras' theorem
In exercise 3 you will find out that it is always true that if you put a square on each side of a right-angled triangle, the area of the smaller squares added up is the area of the biggest square. This is Pythagoras' theorem:
If a and b are the short sides of a right-angled triangle and if c is the hypothenuse, then:
Slide 12 - Tekstslide
Calculating unknown sides
Using Pythagoras' Theorem, you can calculate
the 3rd side of a triangle, if you know the
lengths of the other two sides.
Slide 13 - Tekstslide
Calculating unknown sides
We can use this scheme, to fill in everything
we know about the triangle.
Slide 14 - Tekstslide
Calculating unknown sides
Slide 15 - Tekstslide
Calculating unknown sides
Slide 16 - Tekstslide
Calculating unknown sides
Slide 17 - Tekstslide
Calculating unknown sides
so PR = 12
Slide 18 - Tekstslide
Using Pythagoras' Theorem
When using Pythagoras' Theorem, you need to make sure:
- Your triangle is a right-angled triangle
- You know which sides are the short sides and which side is the hypotenuse, so you can add/subtract the correct squares.
Lesduur is: 50 min
