Cambridge International Mathematics

The theorem of Pythagoras 8 Contents: A Pythagoras’ theorem [4.6] B The converse of Pythagoras’ theorem [4.6] C Problem solving ...

The Egyptians used this procedure to construct their right angles: make rope taut corner line of one side take hold of knots at ...

The theorem of Pythagoras (Chapter 8) 171 There are over 400 different proofs of Pythagoras’ theorem. Here is one of them: On a ...

172 The theorem of Pythagoras (Chapter 8) Example 3 Self Tutor Findxin surd form: ab a The hypotenuse has lengthxcm. ) x^2 =2^2 ...

The theorem of Pythagoras (Chapter 8) 173 2 Find the length of the third side these triangles, giving your answers correct to 3 ...

174 The theorem of Pythagoras (Chapter 8) 9 Find the distance AB in the following: abc Challenge 10 In 1876 , President Garfield ...

The theorem of Pythagoras (Chapter 8) 175 Example 6 Self Tutor Findkiff 9 ,k, 15 gis a Pythagorean triple. Let 92 +k^2 =15^2 fPy ...

176 The theorem of Pythagoras (Chapter 8) If we have a triangle whose three sides have known lengths, we can use theconverseofPy ...

The theorem of Pythagoras (Chapter 8) 177 3 4 Triangle ABC has altitude BN which is 6 cm long. AN=9cm and NC=4cm. Is triangle AB ...

178 The theorem of Pythagoras (Chapter 8) Example 8 Self Tutor A rectangular gate is 3 m wide and has a 3 : 5 m diagonal. How hi ...

The theorem of Pythagoras (Chapter 8) 179 Example 11 Self Tutor An equilateral triangle has sides of length 6 cm. Find its area. ...

180 The theorem of Pythagoras (Chapter 8) 6 A rhombus has diagonals of length 8 cm and 10 cm. Find its perimeter. 7 On the grid ...

The theorem of Pythagoras (Chapter 8) 181 There are certain properties of circles which involve right angles. In these situation ...

182 The theorem of Pythagoras (Chapter 8) Example 14 Self Tutor The shortest distance is the ‘perpendicular distance’. The line ...

The theorem of Pythagoras (Chapter 8) 183 For centres C and D, we draw BC, AD, CD and CEkAB. ) ABCE is a rectangle ) CE=7cm fas ...

184 The theorem of Pythagoras (Chapter 8) 7 A chord of a circle has length 3 cm. If the circle has radius 4 cm, find the shortes ...

The theorem of Pythagoras (Chapter 8) 185 17 A chord AB of length 2 cm is drawn in a circle of radius 3 cm. A diameter BC is con ...

186 The theorem of Pythagoras (Chapter 8) Example 19 Self Tutor A pyramid of height 40 m has a square base with edges 50 m. Dete ...

The theorem of Pythagoras (Chapter 8) 187 9 A 6 mby 18 mby 4 m hall is to be decorated with streamers for a party. 4 streamers a ...

188 The theorem of Pythagoras (Chapter 8) 8 Two circles have the same centre. The tangent drawn from a point P on the smaller ci ...