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Pythagoras’ Theorem. 22/11/2012. Find : (to 1.d.p) 3² = b) 7² = c) 3.45² = d) 9² = e) 10² = f) 20² = g) 2.1 ² = Find: √ 9 = b) √7 = c) √36= d) √2 = e) √1.456 = f) √2.5 g) √64 =.

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3 B’s B4 Me

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#### Presentation Transcript

Pythagoras’ Theorem

22/11/2012

Find: (to 1.d.p)

3² = b) 7² = c) 3.45² = d) 9² =

e) 10² = f) 20² = g) 2.1 ² =

Find:

√9 = b) √7 = c) √36= d) √2=

e) √1.456 = f) √2.5 g) √64 =

3 B’s B4 Me

Pythagoras’ Theorem

22/11/2012

Find:

9 b) 49 c) 11.9d) 81

e) 100 f) 400 g) 4.4

Find:

3 b) 2.6 c) 6d) 1.4

e) 1.2 f) 1.6 g) 8

3 B’s B4 Me

Criteria for Success

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

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

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

Keywords

Pythagoras

Hypotenuse

Square

Right Angle

Square Root

Investigate

Theorem

Prove

3 B’s B4 Me

Pythagoras’ Theorem

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

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

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

3 B’s B4 Me

The Hypotenuse

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

b

a

z

c

x

b

a

y

c

3 B’s B4 Me

Make accurate copies of the three right-angled triangles below

3

1

2

6cm

Can you see a pattern in the last 3 columns?

If you can then you have rediscovered Pythagoras’ Theorem

5cm

Next measure the length of the longest side of each one. Then complete the table under activity one on your sheet!

3cm

a

4cm

b

12cm

8cm

c

4

Using Pythagoras’ Theorem

c

a

Area C

c2

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

b

Area A

a2

Area B

b2

Using Pythagoras’ Theorem

Area C

9 +16 = 25

Find the Length of side x

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

How do we get the length of side x

x =25 = 5cm

Area A

32 = 9

x

3cm

4cm

Area B

42 = 16

Using Pythagoras’ Theorem

Example

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

x

Find the Length of side x

7cm

9cm

1. Complete activity two on your worksheet

2. Complete the questions below

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

A.

B.

3cm

5cm

8cm

7.5cm

5.8cm

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

4.5cm

Now complete activity 3 on the sheet.

And to finish…

x cm

How can we find out the shorter side?

8cm

10cm

### Lesson Outcomes

• 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.

3 B’s B4 Me