3 b’s b4 me
DESCRIPTION
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 =. - PowerPoint PPT PresentationTRANSCRIPT
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.