1. The Theorem Of Pythagoras.c
Pythagoras was a Greek Mathematician.( B.C) years old is even older than your teacher.
He was eccentric. (mad!!) Don’t mention √ 2 to him!!
He discovered an amazing rule about right angled triangles.
By completing the table opposite you are going to make the discovery for yourself. b a a b c a2 b2 c2 3 4 5 12 6 10 8 15

2. Complete the results of your table below:3 4 5 12 6 8 15 5 9 16 25 13 25
144
169 10 36 64
100 17 64
225
289
By considering all the numbers in the completed table can you see what Pythagoras discovered ?
The Theorem Of Pythagoras: a2 + b2 = c2

3. Calculating An Unknown Side.
The longest side of a right angled triangle is called the hypotenuse.
HYPOTENUSE c a
Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. b a2 c2 + b2 =

4. Find the side A in this triangle.6 8
Hint
Follow this routine exactly every time to solve Pythagoras problems easily.
Solution.
A2 =
A2 =
A2= 100
A = √100
A =10

5. What Goes In The Box?
Find the length of side W in this right angled triangle. W
6.4cm
5.8cm W2 +
5.82 =
6.42 = W2
40.96 +
33.64 W2 =
74.6 W =
74.6 W =
8.6cm

6. Find the unknown side in each of the triangles below.
(2) 6 7 B 9
(1) 8 A
12.04
9.22
(3) 23 9 C
10.73
24.7
(4)
6.8
8.3 D
(5)
8.9
22.7 E
24.38

7. Finding A Shorter Side. Calculate the length of side W.
14.7m
W =
W2 = – W
W = √ 64.8
W = 8.05 m
12.3m

8. What Goes In The Box? 2
Find the length of side H in the right angled triangle below: H
3.4m
2.6m +
2.62 =
3.42 H2
6.76 =
11.56 H2 + -
6.76 H2 =
11.56 H2 =
4.8 H =
4.8 H =
2.19m

9. Calculate the size of the shorter side in the following.
13.59m
9.2cm
(2)
14.4m
19.8m B
12.4cm
(1)
8.3cm A
(3)
11.2mm
6.7mm C
9mm
(5)
14.7cm
8.6cm E
27.6m
(4)
35.7m
22.6m D
11.9cm