1. Pythagoras' Theorem

2. Starter In your book, Draw a Horizontal Line measuring 4cm
Then, on one end of the line, draw a 3cm Vertical line
What is the distance between the two unjoined ends?

3. Pythagoras’ Theorem
Pythagoras’ Theorem links the lengths of 3 sides of a Right Angled Triangle
The formula is:
a² + b² = c² c a b

4. Pythagoras’ Theorem c
a² + b² = c² a b
It does not matter which way round we put a and b, as long as side c is the longest side
We call side c the HYPOTENUSE
It is always opposite the right angle

5. Pythagoras’ Theorem Find the length of the missing side… a² + b² = c²
7.21cm = c
7.21cm c b
6cm
4cm a
(square root both sides)
(to 2 d p)

6. Pythagoras’ Theorem Find the length of the missing side… a² + b² = c²
13.6cm = c
11cm
8cm c
13.6cm
(square root both sides)
(to 1 d p)

7. Plenary
a2 + c2 = b2

8. Plenary
Because 75º + 25º = 100º, so the missing Angle is 80º. Pythagoras’ Theorem only works in Right-Angled Triangles

9. Pythagoras’ Theorem Finding a shorter side…c
Find the length of the missing side…
c² b² = a²
8² ² = a²
= a²
28 = a²
… = a
5.29cm = a
8cm b
6cm
5.29cm a
(square root both sides)
(to 2 d p)

10. Pythagoras’ Theorem Finding a shorter side…b a
10.82cm
2cm
Find the length of the missing side…
c² a² = b²
11² ² = b²
= b²
117 = b²
= b
10.82cm = b
11cm c
(square root both sides)
(to 2 d p)

11. Plenary
In your books, sketch a set of axes and plot on them the coordinates (2,1) and (5,8)
Calculate the distance between the 2 coordinates
(5,8)
(2,1)
a2 + b2 = c2 7
= c2
58 = c2 3
7.62 = c

12. Summary
We have learnt how to use Pythagoras’ Theorem to find missing sides in right-angled triangles
Next lesson we will look at some worded questions