content- by the end of the lesson we will… be able to understand and use pythagoras’ theorem...

Learning Outcomes –

Using Pythagoras’ Theorem

CONTENT- By the end of the lesson we will…be able to understand and use Pythagoras’ Theorem

PROCESS- We will know we are successful… All will work together to understand Pythagoras’ Theorem and how

it relates to a triangle

Most will work in pairs to use Pythagoras Theorem to find missing sides on a triangle Rally coach

Some will be able to use these skills to solve written real-life problems using Pythagoras Theorem and assess each other’s

answers using Carousal feedback

BENEFITS- We are learning this because…3000 years ago the Egyptians used Pythagoras Theorem to build the Great Pyramids using knotted rope to make a 90o angle using a 3,4,5 triangle. Today builders using pieces of

wood with length 3ft, 4ft, 5ft to the same thing to get a perfect 90o right angle

Level 7

Level 8

Pythagoras’ Theorem

I was born at Samos, in Greece, and lived from 580 to 500 B.C.

Now you are going to try to find out what I discovered!!

I was a Mathematician who became famous for discovering something unique about right – angled triangles.


Make accurate copies of the three right-angled triangles below

4cm

3cm

12cm

5cm

8cm

6cm

Next measure the length of the longest side of each one. Then complete the table below

a b c a2 b2 c2

3 4

5 12

6 8

1 2 3

4b

ac

Can you see a pattern in the last 3 columns? .

If you can then you have rediscovered Pythagoras’ Theorem


Make accurate copies of the three right-angled triangles below

4cm

3cm

12cm

5cm

8cm

6cm

Next measure the length of the longest side of each one. Then complete the table below

a b c a2 b2 c2

3 4

5 12

6 8

1 2 3

4b

ac

Can you see a pattern in the last 3 columns?

5

13

10

9 16 25

25 144 169

36 64 100

a2 + b2 = c2


So what is Pythagoras’ Theorem?

He said that:

“For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.”

Pythagoras

a2 + b2 = c2 a

b

cArea A

a2

Area B

b2

Area C

c2


We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle

Area A

32 = 9

Area B

42 = 16

Area C

9 +16 = 25

3cm

4cm

xWe SQUARE to get the area of the smaller squares

Find the Length of side x

We ADD to get the area of the biggest square

How do we get the length of

side xWe SQUARE ROOT the area to get the length of side x

x =25 = 5cm


1. Square


2. Add

7cm

9cm

x

3. Square x = 130Root x = 11.4cm

x2 = 130

92 = 8172 = 49


Example 1

Level 7


1. Square


2. Add

4cm

8cm

x

3. Square x = 80Root x = 8.9

x2 = 80

82 = 6442 = 16


Example 2

Level 7


1. Square


2. Subtract

12cm

7cm

x

3. Square x = 95Root x = 9.7cm

x2 = 95

122 = 144 72 = 49

We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle

Example 3

Level 7


1. Square


2. Subtract

23mm15mm

x

3. Square x = 304Root x =

17.4cm

x2 = 304

232 = 529 152 = 225

We can use Pythagoras’ Theorem to find a Short side in a right –angled triangle

Example 4

Level 7


1

25cm

60cm

219m

14m

3

5cm

11cm

For each of the following triangles, calculate the length of the missing side, giving your answers to one decimal place when needed.

4 5 6

12mm

13mm

1.5cm1.1c

m

3cm

6cm

Answer = 6.7cm Answer = 9.8cm Answer = 23.6m

Answer = 5mm Answer = 1.0cm Answer = 65cm

I have met todays Learning Outcome : Level 7

Answer = 8.5cm Answer = 16.1cm

7 8Calculate the length of the diagonal of this square.

6cm

If a right angle has short lengths 14cm and 8cm, what is the length of the longest side.

9

12cm12cm

8cm

10 Calculate the base of this isosceles triangle.

10cm10cm

8cm

Calculate the height of this isosceles triangle.

Answer = 11.3cm

Answer = 12cm

I have met todays Learning Outcome :


• Each team-mate has a different real – life problem. • On your own solve each of these problems. • Once you completed, swap with the other pupils on your table and give

feedback each others answers


Real Life Problem 1A boat travels 45 miles east then 60 miles north, how far is it from where it started? (hint: draw a diagram)

A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they have swam? (hint: draw a diagram)

Real Life Problem 2

Answer = 75miles

Answer = 27.7m

Level 8


Real Life Problem 3A ladder which is 4m long leans against a wall, the bottom of the ladder is 1.5m from the bottom of the wall, how high up the wall does the ladder go? (hint: draw a diagram)

A rope of length 10m is stretched from the top of a pole 3m high until it reaches the ground. How far is the end of the rope to the base of the pole.(hint: draw a diagram)

Real Life Problem 4

Answer = 3.7m

Answer = 9.5m

Level 8

content- by the end of the lesson we will… be able to understand and use pythagoras’ theorem...

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