Cambridge International Mathematics

174 The theorem of Pythagoras (Chapter 8)

9 Find the distance AB in the following:

abc

Challenge

10 In 1876 , President Garfield of the USA published a proof of

the theorem of Pythagoras. Alongside is the figure he used.

Write out the proof.

11 You are given a rectangle in which there is a point that is

3 cm, 4 cm and 5 cm from three of the vertices. How far is

the point from the fourth vertex?

PYTHAGOREAN TRIPLES

The simplest right angled triangle with sides ofintegerlength is the

3-4-5 triangle.

The numbers 3 , 4 , and 5 satisfy the rule 32 +4^2 =5^2.

The set of positive integersfa,b,cgis aPythagorean tripleif it obeys the rule

a^2 +b^2 =c^2 :

Other examples are: f 5 , 12 , 13 g, f 7 , 24 , 25 g, f 8 , 15 , 17 g.

Example 5 Self Tutor

Show that f 5 , 12 , 13 g is a Pythagorean triple.

We find the square of thelargestnumber first.

132 = 169

and 52 +12^2 = 25 + 144 = 169

) 52 +12^2 =13^2

So,f 5 , 12 , 13 gis a Pythagorean triple.

B

N

M

A

1m

5m

3m

A B

4m

6m 7m

A D

B

E

a

b a

b

c

c

C

4cm 3cm

xcm

5cm

(^53)
4
D C
A
B
4cm 3cm
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Y:\HAESE\IGCSE01\IG01_08\174IGCSE01_08.CDR Friday, 10 October 2008 4:45:36 PM PETER