Unit 9 Answers. Exercise 9.1. KS3 Maths Progress Delta 2. 1 a 200 cm b 6.2 m c 1.35 km 2 a 25 cm. b 300 cm. c 75 cm d 22.5 cm 3
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1 Exercise a 200 cm b 6.2 m c 1.35 km 2 a 25 cm b 30 cm c 75 cm d 22.5 cm 3 4 a 1800 m b 1440 m c 5400 m d 720 m 5 a 20 cm b 300 cm c 45 cm d 50 cm e 250 cm f 450 cm 6 a i 250 m ii 150 m iii 100 m b 6 minutes 7 a 1 cm on the map is 200 km in real life. b i 300 km ii 540 km iii 900 km 8 Angle is 78 9
2 Exercise Angles accurately drawn. 2 a a = 323 b b = 98 c c, d = 70 3 a 120 km b 6 cm 4 a 090 b 180 c 270 d 135 e 225 f a 115 b a b Bearing 095, distance 104 km
3 8 a b 7 km 9 a b 40 miles c a 300 b 060 c Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
4 Exercise a 250 m b 400 m c 1 km d 1.5 km 2 a 1 : 5 b 1 : 3 c 1 : 15 d 1 : 10 3 a 300 b 150 c 1000 d a 800 m b 1200 m c 900 m d 100 m 5 A iv B i C iii D ii 6 a i 1.7 cm ii 8.5 km 6 b i 12.5 km ii 5 km iii 15.5 km 7 a, b c 18 m 2 8 a 1: 100 b 1 : c 1: d 1: a i 400 m
5 ii 2 km iii 10 km b i 100 cm ii 20 cm iii 4 cm 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
6 Exercise a 2 b a a = c and b = d (vertically opposite). b a = c and b = d (alternate angles). 3 A and C, B and E are congruent. 4 5 a SAS b SSS c ASA 6 DEF congruent SSS HGI congruent SAS JKL not congruent because the 93 angle is adjacent to the 4.2 cm dimension, not opposite to it. 7 Yes because SAS 8 a x = y (vertically opposite angles) b c Angle AEB = Angle CED (vertically opposite) Angle BAE = Angle EDC (alternate angles) Angle ABE = Angle ECD (alternate angles) AB = CD As all angles are the same and one side is equal, the two triangles are congruent. 9 Angle BAC = 85 which is equal to angle EDF Angle EFD = 30 which is equal to angle BCA As all angles are the same the triangles are similar cm 11 a a = 4.5, b = 2 b c = 2.5 cm, d = 2.4 cm 12 A and C are similar.
7 Exercise No, they are not similar. 2 x = 5 cm 3 a Vertically opposite b d is equal to b alternate angles c c is equal to f alternate angles 4 a Angle DCE = 47 vertically opposite Angle CDE = 74 alternate angles Angle CED = 59 alternate angles b As all angles are the same the triangles ABC and CDE are similar. c 5 a Angle MPN = Angle QPR vertically opposite Angle NMP = Angle PRQ alternate angles Angle MNP = Angle PQR alternate angles As all angles are the same the two triangles are similar. b 6 cm 6 a Angle AEC = Angle BDC Angle CAE = Angle CBD = 90 Angle DCB = Angle ECA As the triangles have the same angles they are similar. b 6 cm c 4 cm 7 a Angle ACB = Angle AED Angle ABC = Angle ADC Angle BAC = Angle DAE = 36 As the triangles have the same angles they are similar. b 14 cm c 7 cm d 3 cm m
8 9 Check up Maps and scales 1 48 cm cm 3 a 250 m b 8 cm m Bearings a b 18 km c 285 Congruence and similarity 7 A and C as they are SAS 8 b x = 8 cm c y = 6 cm 9 Angle AED = Angle ACB = 90 Angle ABC = Angle ADE Angle A is the same in both AAA so are similar 10 a Angle DAE = Angle BAC, vertically opposite Angle DEA = Angle ACB, alternate angles Angle EDA = Angle ABC, alternate angles AAA, so are similar b a = 10 b = 3 Challenge 12 a Yes (AAA) b Yes (AAA)
9 9 Strengthen Maps and scales 1 2 a 2 cm b 6 cm c 20 cm d 40 cm e 20 cm 3 a 20 m b 4 m c 4 m by 8 m 4 a 100 cm b 200 cm c 460 cm d 840 cm 5 a 1.4 km b 1.5 km c 2.15 km 6 a 1 : 100 b 1 : 20 c 1 : 100 d 1 : 300 e 1 : Bearings 1 a 048 b 075 c 170 d 240
10 2 3 4 a 285 b 000 c 075 d a, b 5 c i 14 km ii 320 Congruence and similarity 1 B 2 b i congruent ASA ii similar AAA iii congruent SAS 3 a P Q x 13 y b 2 c x = 24, y = a = 16 cm b = 3 cm c = 9 cm d = 6 cm 6 C and E 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
11 7 a i Alternate angles ii Alternate angles iii Vertically opposite angles b They are similar c x = 4 cm, y = 10 cm 8 a BC and DE are parallel because both are at right angles to AE b Angle ABC = angle ADE because triangles ABC and ADE are similar (AAA) c 2 d 20 cm Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
12 9 Extend 1 a, b c 4.5 km 2 a 1: b 1 : c 3 : a i 135 km ii 75 km iii 145 km b 3 hours 40 minutes c Roads aren t straight, so the actual distance travelled will be greater. 4 a i 40 J ii 30 J iii 10 J b i ii 5 a 1 cm to 20 m b 8000 m 2 c 600 m 2 d
13 6 a Students own accurate scale drawing made using an appropriate scale. b 40 m 2 c 160 d a 105 b 105 c 35 d All angles are the same and all sides are the same. 8 a 8 cm b 4.5 cm c 85 d 5 cm e 45 9 a 5 cm b 15 cm 10 Memmingen 11 a b No 12 a Bearing back to port is 230 b Bearing back to airport is x = 6 cm, y = 12.5 cm 14 Angle B = Angle D Angle BAC = Angle ACD alternate angles Angle DAC = Angle BCA alternate angles Side AD = Side BC 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
14 AAA and a side the same must be congruent 15 OC is a side of both triangles Side OB = OA as both radii so triangle ABO is an isosceles triangle. Angle OBC = Angle OAC Angle BOC = Angle AOC As all angles are the same and two pairs of sides are the same, must be congruent. Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 3
15 9 Unit test 1 a 095 b 150 c Kalimnos 2 a 100 m b 250 m c 12.5 m 3 a 3 cm b 8 cm c 20 cm d 0.2 cm 4 a 1000 m b 325 m 5 a b 29 km c a = 80, b = 6 cm, c = 8cm, d = 80, e = 6 cm, f = 35, g = 80 b 6 cm side is between angles of 35 and 80 in A, B and C. 7 a a = 5 cm b b = 12.8 cm c c = 12.5 cm 8 a a = 7 cm b b = 9 cm, c = 12 cm c d = 15 cm, e = 24 cm, f = 21 cm 9 a Angle ACE is the same in both triangles Angle BDC = Angle AEC corresponding angles Angle DBC = Angle EAC corresponding angles As the angles are the same the triangles are similar. b c 5 10 Triangle SXT and triangle VXU are congruent. Angle SXT = Angle VXU vertically opposite
16 Angle TSU = Angle SUV alternate angles Angle STV = Angle TVU alternate angles Side ST = VU AAA and side equal, so must be congruent. Triangle SXV and triangle TXU are congruent. Angle SXV = Angle TXU vertically opposite Angle VSU = Angle SUT alternate angles Angle VTU = Angle SVT alternate angles Side SV = side TU AAA and side equal so must be congruent. Challenge 11 No, right-angled angles need only have one common angle. 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.
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