Cambridge International Mathematics

176 The theorem of Pythagoras (Chapter 8)

If we have a triangle whose three sides have known lengths, we can use theconverseofPythagoras’

theoremto test whether it is right angled.

THE CONVERSE OF PYTHAGORAS’ THEOREM

If a triangle has sides of lengtha,bandcunits and a^2 +b^2 =c^2 ,

then the triangle is right angled.

Example 7 Self Tutor

Is the triangle with sides 6 cm, 8 cm and 5 cm right angled?

The two shorter sides have lengths 5 cm and 6 cm.

Now 52 +6^2 = 25 + 36 = 61, but 82 =64:

) 52 +6^26 =8^2 and hence the triangle is not right angled.

EXERCISE 8B

1 The following figures are not drawn to scale. Which of the triangles are right angled?

abc

de f

2 The following triangles are not drawn to scale. If any of them is right angled, find the right angle.

abc

THE CONVERSE OF PYTHAGORAS’ THEOREM

[4.6]

B

GEOMETRY

PACKAGE

7cm

4cm

5cm

9cm

15 cm

12 cm

5cm

8cm

9cm

15 m

8m

17 m

3cm

~` 1 ` 2 cm

~` 7 cm

~` 7 ` 5 m

~` 27 ` m ~` 48 ` m

A

B C

8m ~` 2 ` 0 ` 8 m

12 m

A

B C

2 cm 1cm

~` 5 cm

A

B

C

5km

7km

~` 2 ` 4 km

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Y:\HAESE\IGCSE01\IG01_08\176IGCSE01_08.CDR Tuesday, 16 September 2008 11:07:50 AM PETER