Pythagoras (t2a)

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

Pythagoras

February 13th, 2023

t2a

8:30

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Schedule

• Programme                                                                 5 min
• Pythagoras                                                               20 min
   Quiz questions
• Practice                                                                     25 min
  
• Gooseboard!                                                           25 min

Programme

Today's

Intended Learning Outcomes

At the end of the lessons you can...

• Use and recognize Pythagoras's Theorem to:
           Calculate the hypotenuse in right-angled triangles
           Calculate distances in coordinate systems
           Recognize Pythagoras in pictures or stories

What do you know about
Pythagoras?

Right-angled triangles

A right-angled triangle always has two legs and one hypotenuse

The hypotenuse is always opposite the right angle

Pythagoras's theorem

1. Take any right-angled triangle
2.  
3.  

Pythagoras's theorem

1. Take any right-angled triangle
2. Stick a square to each side
3. 
   

Pythagoras's theorem

1. Take any right-angled triangle
2. Stick a square to each side
3. The theorem:
   Add up the areas of the squares
   stuck to the legs...
    

Pythagoras's theorem

1. Take any right-angled triangle
2. Stick a square to each side
3. The theorem:
   Add up the areas of the squares
   stuck to the legs...
   ...and the answer is the area of the
   square stuck to the hypotenuse!

Pythagoras's theorem

1. Take any right-angled triangle
2. Stick a square to each side
3. The theorem:
   Add up the areas of the squares
   stuck to the legs...
   ...and the answer is the area of the
   square stuck to the hypotenuse!

What is the area of the
green square?

1. 6.5
2. 42
3. 52
4. 102

How long is the side that the
green square is stuck to?

1. 6.5
2. 8.5
3. 10.3
4. 42.0

A bit more mathematical...

A bit more mathematical...

AB​2​​+AC​2​​=BC​2​​

A bit more mathematical...

Let's say AB = 4 and AC = 6.

How do you calculate BC?

AB​2​​+AC​2​​=BC​2​​

AB = 3 and AC = 4.
Calculate BC.

1. BC=√​34​​​
2. BC=7
3. BC=5
4. BC=1

Distances

Distances

Calculate the distance between
C(2, 7) and D(4, 11).
Round to one decimal place.
Tip: make a sketch!

1. CD=6
2. CD=20
3. CD=2.4
4. CD=4.5

Try it yourself

Calculate the distance between

C(2, 7) and D(4, 11).

Round to one decimal place.

Tip: make a sketch!

Calculate the distance between
C(2, 7) and D(4, 11).
Round to one decimal place.
Tip: make a sketch!

1. CD=6
2. CD=20
3. CD=2.4
4. CD=4.5

Practice

Chapter 5:

Basic route

5, 9, 10, 13, 14, 15, 18

Advanced route

5, 9, 11, 13, 14, 16, 18

Gooseboard!

Which one do you prefer?

Practice with the basics

Practice with the coordinate systems