313A
Guided practice worksheet
�3 14.1 Constructing triangles
1 Here is a sketch of triangle ABC.
Construct an accurate drawing of triangle ABC.
2 Here is a sketch of triangle XYZ.
Construct an accurate drawing of triangle XYZ.
6.5 cm
7 cm
C
A B
5 cm
3 cm
4 cm
Z
Y X
5 cm
Start with the base AB = 6.5 cm. Then open the pair of compasses to 5 cm and draw an arc, centre A.
Questions are targeted at the grades indicated
D
�3 14.1 Constructing triangles
313B
3 Here is a sketch of the triangle PQR.
Construct an accurate drawing of the triangle PQR.
4 Construct an equilateral triangle with sides of length 4.5 cm.
Guided practice worksheet
Hint It is a good idea to draw a sketch � rst.
8 cm5cm
5cmP Q
R
D
�3 14.1 Constructing triangles
313C
5 Construct the triangle ABC with sides AB = 4.5 cm, BC = 5.5 cm and CA = 5.5 cm.
6 Construct the triangle PQR with sides PQ = 4.8 cm, QR = 5.8 cm and RP = 6.8 cm.
Guided practice worksheet
D
�3 14.1 Constructing triangles
313D
7 Construct triangle XYZ with sides XY = 4.0 cm, YZ = 5.8 cm and ZX = 7.1 cm.
8 Here is a sketch of the quadrilateral CDEF.
Make an accurate drawing of quadrilateral CDEF.
Guided practice worksheet
3.2 cm
4.5 cm
5.5 cm4 cm
6.4 cm
E
DC
F
D
�3 14.2 Perpendicular lines
315A
1 Construct the perpendicular bisector of each of the lines AB.
2 Construct the perpendicular bisector of each of the lines XY.
Guided practice worksheet
Draw arcs above and below the line to be bisected.
A B
A B
A B
A B
A B
A B
A B
A B
A B
X Y
X
Y
X
Y
X Y
X
Y
X
Y
X Y
X
Y
X
Y
C
Questions are targeted at the grades indicated
�3 14.2 Perpendicular lines
315B
3 Construct the perpendicular from the point P on the line AB in each of the following cases.
4 Construct the perpendicular from the point P to the line AB in each of the following cases.
Guided practice worksheet
A BP
B
P
A
A
P
B
A
A
B
B
P
A
B
P P
A
A
B
B
P
A
B
P P
Remember to start by drawing arcs, centre P, which cut AB on either side of P.
Remember to draw arcs, centre P, to cut AB.
C
�3 14.2 Perpendicular lines
315C
5 Construct the perpendicular from P to the side QR of the triangle PQR in each case.
Guided practice worksheet
Q
P R Q R
P
C
�3 14.3 Constructing and bisecting angles
317
1 In each case, construct the bisector of the angle ABC. Remember to start by drawing arcs centre B to cut BA and BC.
A
B C
C
C
B
B
B
C
A
A
A
A
B C
C
C
B
B
B
C
A
A
A
Guided practice worksheet
C
Questions are targeted at the grades indicated
A
B C
C
C
B
B
B
C
A
A
A
A
B C
C
C
B
B
B
C
A
A
A
�3 14.4 Loci
319A
1 Draw the locus of all points that are equidistant from X and Y.
2 Draw the locus of all points that are equidistant from C and D.
3 Draw the locus of all points that are 1.5 cm from the point P.
4 Draw the locus of all points that are 3 cm from the line segment AB.
Guided practice worksheet
X Y
C
D
A B
P ×
Think what property the perpendicular bisector of XY has.
Hint Think about the shape this will produce.
Remember to think carefully about what happens at the ends, A and B
C
Questions are targeted at the grades indicated
�3 14.4 Loci
319B
5 Draw the locus of all points that are equidistant from the lines PQ and PR.
Guided practice worksheet
P
R
Q
C
�3 14.5 Regions
321A
1 Shade the region of points that are less than 2.5 cm from the point P.
2 Shade the region of points less than 1.8 cm from the line segment AB.
3 Shade the region of points closer to C than D.
4 Shade the region of points closer to the line AB than to the line AC.
Guided practice worksheet
P ×
A B
C ×
D ×
A C
B
Think carefully about what to do about the points A and B.
C
Questions are targeted at the grades indicated
�3 14.5 Regions
321B
5 Show, by shading, the region of points more than 1.6 cm from the point Q.
Guided practice worksheet
Q ×
C
�3 14.6 Bearings
323A
1 Measure and write down the bearing of B from A.
a b c d e
.................................. .................................. .................................. .................................. ..................................
2 Use the protractor to draw diagrams of the following bearings.
a The bearing from A to B is 075°. b The bearing of C to D is 210°.
c The bearing from E to F is 148°.
N
A
B
N
A
B
N
A
B
N
A
N
B
NN
B
A
N
A
B
N
A
B
N
A
B
N
A
N
B
NN
B
A
N
A
B
N
A
B
N
A
B
N
A
N
B
NN
B
A
N
A
B
N
A
B
N
A
B
N
A
N
B
NN
B
A
N
A
B
N
A
B
N
A
B
N
A
N
B
NN
B
A
Guided practice worksheet Questions are targeted at the grades indicated
�3 14.6 Bearings
323B
3 The bearing of x from y is 067°. Work out the bearing of y from x.
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4 The bearing of Heathrow airport from a plane is 237°.
Work out the bearing of the plane from Heathrow airport.
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5 The bearing of a lighthouse from ship A is 307°. The ship is 5 km from the lighthouse. The bearing of a second ship B from ship A is 270°. Ships A and B are 4 km apart.
a Draw a scale diagram showing the positions of the two ships.
b How far away from the lighthouse is ship B?
.....................................................................................................
6 A boat leaves a port on a bearing of 069°.
Work out the bearing the boat needs to use to return to port.
..............................................................................................................................
Guided practice worksheet
D
Hint Use a scale of 1 cm = 1 km
�3 14.7 Scale drawings and maps
325A
1 The Eiffel tower is 324 m high. A model has a scale of 1 : 400. Calculate its height.
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2 A map has a scale of 1 : 50 000. Karen measured the following distances on the map. What are the distances in the real world, in km?
a Snedbury to Fley 9 cm
.................................................................................................................................................................................................................................
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b St John’s Church to Kipley Cross 2.5 cm
.................................................................................................................................................................................................................................
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c Draybridge to Gleet 29 cm
.................................................................................................................................................................................................................................
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d Bridge to Weir 17 mm
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3 A central London map has a scale of 1 : 11 500. Find the distance on the map, in cm, for each real distance given below. Work to the nearest mm.
a Piccadilly Circus to Parliament Square 1.9 km ..............................................................................................................................
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b Marble Arch to Hyde Park Corner 2.07 km .......................................................................................................................................
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Guided practice worksheet
Newton to Crotchley 12 cm Real world distance = 50 000 × 12 cm = 600 000 cm = 6 km
D
Trafalgar Square to To� enham Court Road 1.5 km 1.5 km = 1.5 × 1000 m = 150 000 cm Map distance = 150 000 cm ÷ 11 500 = 13.0 cm (to nearest mm)
Questions are targeted at the grades indicated
�3 14.7 Scale drawings and maps
325B
Guided practice worksheet
c British Library to Oxford Circus 1.84 km ............................................................................................................................................
.................................................................................................................................................................................................................................
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d Covent Garden to Leicester Square 520 m .......................................................................................................................................
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4 The body of a Chinook helicopter is 52.1 m long. A scale model is 20.8 cm long.
a Find the ratio of the scale model in the form 1 : n
.................................................................................................................................................................................................................................
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b The rotor blade length is 30.2 m. Find the width of the model, to the nearest mm.
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5 This Pearson logo was enlarged so that its length was 1.7 m.
a Find the scale of the enlargement in the form 1 : n
.................................................................................................................................................................................................................................
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b Find the height of the enlargement, to the nearest cm.
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D
C
�3 14.7 Scale drawings and maps
325C
Guided practice worksheet
6 This map of the Isle of Wight has a scale of 1 : 500 000
i Measure the distance between the two towns, in cm, to 1 decimal place.
ii Calculate the real distance between the towns, in km.
a Cowes to Ryde i .................................................................. ii ..................................................................
b Ryde to Sandown i ................................................................. ii ..................................................................
c Sandown to Shanklin i .................................................................. ii ..................................................................
d Newport to Freshwater i ................................................................. ii ..................................................................
e Freshwater to Ventnor i .................................................................. ii ..................................................................
f Ventnor to Cowes i .................................................................. ii ..................................................................
g Bembridge to Freshwater i .................................................................. ii ..................................................................
h Sandown to Ventnor i .................................................................. ii ..................................................................
7 This is a plan of an art gallery.
a The East wall has a real length of 12 m. Find the scale of the map in the form
i 1 cm represents n m ..................................................................................................................................................................................
ii 1 : n ............................................................................................................................................
C
Eastwall
Freshwater
Northwood
Cowes
Ryde
Seaview
Bembridge
Sandown
Shanklin
Ventnor
Newport
D
�3 14.7 Scale drawings and maps
325D
Guided practice worksheet
b Draw an accurate scale drawing on centimetre squared paper. C