3 B’s B4 Me

Find: (to 1.d.p) a) 3² = b) 7² = c) 3.45² = d) 9² =

e) 10² = f) 20² = g) 2.1 ² =  Find:  b) √9 = b) √7 = c) √36= d) √2=

e) √1.456 = f) √2.5 g) √64 =

Pythagoras’ Theorem

22/11/2012

3 B’s B4 Me

Find: a) 9 b) 49 c) 11.9 d) 81

e) 100 f) 400 g) 4.4 Find:  b) 3 b) 2.6 c) 6 d) 1.4

e) 1.2 f) 1.6 g) 8

Pythagoras’ Theorem

22/11/2012

Criteria for Success

• To know what Pythagoras theorem is and use it to find the length of the hypotenuse

• To find out what Pythagoras proved using powers of investigation!

• To know how to use Pythagoras theorem to show whether a triangle is right-angled.

Square Right Angle

Prove

Hypotenuse

Investigate

Pythagoras

Theorem

Keywords

Square Root

3 B’s B4 Me

3 B’s B4 Me

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.

3 B’s B4 Me

The longest side opposite the right angle is called the hypotenuse.

The Hypotenuse

x

a

y

a

z

b

b

c

c

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 under activity one on your sheet!

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

Using Pythagoras’ Theorem

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

= c2a

b

cArea A

a2

Area B

b2

Area C

c2

Using Pythagoras’ Theorem

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

x

Find the Length of side x

How do we get the

length of side x

x =25 = 5cm

Using Pythagoras’ Theorem

Find the Length of side x

7cm

9cm

x

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

Example

Applying your knowledge

1. Complete activity two on your worksheet 2. Complete the questions below

3. Begin activity three! See how far you can get!

All about the right-angle…

5cm 3cm

5.8cm

8cm

7.5cm

A. B.

4.5cmOne of these is a right-angle, how do we show which one?

Now complete activity 3 on the sheet.

And to finish…

8cmx cm

10cm

How can we find out the

shorter side?

I am able to apply my knowledge of maths to different situations.

I can calculate a missing hypotenuse on a right-angled triangle

I am able to use Pythagoras to identify whether a triangle has a right angle.

Lesson Outcomes

3 B’s B4 Me

Next to the title, rate (from 1-5) how confident you feel that you have achieved

the learning outcomes. 5 being very confident, and one being not confident at

all.