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3 B’s B4 Me

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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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slide1

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

slide2

Pythagoras’ Theorem

22/11/2012

Find:

9 b) 49 c) 11.9 d) 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

slide3

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!
slide4

Keywords

Pythagoras

Hypotenuse

Square

Right Angle

Square Root

Investigate

Theorem

Prove

3 B’s B4 Me

slide5

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

slide6

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

slide7

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

slide8

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

slide9

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

slide10

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

slide11

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!

slide12

All about the right-angle…

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.

slide13

And to finish…

x cm

How can we find out the shorter side?

8cm

10cm

lesson outcomes
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

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