# 1819 C2X §6.1

Which exercises/theories should we discuss on the board?
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Slide 1: Mind map
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This lesson contains 20 slides, with interactive quiz and text slides.

Lesson duration is: 50 min

## Items in this lesson

Which exercises/theories should we discuss on the board?

#### Slide 1 -Mind map

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 -Slide

Exercise 2
2a) Which sides are the shorter sides
of triangle ABC?

#### Slide 3 -Slide

Exercise 2
2a) Which sides are the shorter sides
of triangle ABC?

AB and AC

#### Slide 4 -Slide

Exercise 2
2b) Calculate the area of square
ACHI and the area of square ADEB

#### Slide 5 -Slide

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 -Slide

Exercise 2
2c) Calculate the area of square
BFGC by enclosing the square

#### Slide 7 -Slide

Exercise 2
2c) Calculate the area of square
BFGC by enclosing the square

Area BFGC = 25

#### Slide 8 -Slide

Exercise 2
2d) Add the areas of square ACHI
and square ADEB together.
What do you notice?

#### Slide 9 -Slide

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 -Slide

Exercise 2
2e) Calculate the lenght of BC

Area of the square is 25, so the
lenght of BC =

#### Slide 11 -Slide

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 -Slide

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 -Slide

Calculating unknown sides
We can use this scheme, to fill in everything
we know about the triangle.

#### Slide 14 -Slide

Calculating unknown sides

#### Slide 15 -Slide

Calculating unknown sides

#### Slide 16 -Slide

Calculating unknown sides

#### Slide 17 -Slide

Calculating unknown sides

so PR = 12

#### Slide 18 -Slide

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.

#### Slide 19 -Slide

HW Tuesday
Make and correct §6.1