Pythagoras’ Theorem
WALT: To explore Pythagoras’
theorem
Number Recap
What does success look like?
WILF
Success Criteria
To identify the hypotenuse of a
triangle and correctly label the
sides and recall Pythagoras’ theorem
The hypotenuse of a triangle is…
You use Pythagoras when…
To apply Pythagoras’ theorem to
find the longest side of a right
angled triangle
To find a missing side that is not the
hypotenuse
Apply your knowledge to worded and
real life contexts
x
3
4
10
x
8
Key words
•
•
•
•
•
•
Right angled triangle
Hypotenuse
Square
Square root
Length
Pythagoras
Who is Pythagoras?
Pythagoras was a Greek philosopher and
mathematician who was born in 570 BC.
He came up with a number of mathematical
discoveries.
We are going to learn one of them today
surrounding triangles.
The hypotenuse
Label the sides as a b and c where c is
the hypotenuse
http://www.youtube.com/watch?v=CAkMUdeB06o&feature=related
c
b
a
c2 = a2 + b2
Proof
9
9
The formula
c
a
b
a2 + b2 = c2
Simple example
x
3cm
4cm
copy
Rally Coach
Partner B writes, Partner A explains
Partner A writes, Partner B explains
12cm
5cm
6cm
8cm
11cm
10cm
8cm
4cm
Rally Coach
Partner B writes, Partner A explains
Partner A writes, Partner B explains
12cm
Answer = 10cm
6cm
5cm
Answer = 13cm
8cm
11cm
Answer =
10.77cm
Answer = 13.6cm
10cm
8cm
4cm
What is being done wrong?
What if we want to find a shorter side?
5cm
3cm
y
Rally coach Calculator allowed
Partner A writes, Partner B explains
Partner B writes, Partner A explains
x
15cm
x
7cm
18cm
8cm
12cm
4cm
x
x
20cm
8cm
Ladder against a wall problem
Proof
?
9
7.81cm
5cm
y
y
12m
7m
7m
Height = ?
4m
(2,20)
B
A
(-2, 5)
Calculate the length of the line AB
Worded problem
At an obstacle course contenders have to walk
along a ladder that extended 25m in length and
is placed 24m away from the tyres that are
supporting it. How high off the ground are you if
you walk to the end of the ladder and stand on
top of the tyres? (Draw a diagram to help you)