3 12.1 ongruent triangles Questions are targeted at the grades indicated 1 re these two triangles congruent? Justify your answer. 70 70 80 30 R Q 2 re these two triangles congruent? Justify your answer. 70 70 80 R 30 Q 3 re these two triangles congruent? Justify your answer. R 30 Q 297
3 12.1 ongruent triangles 4 re these two triangles congruent? Justify your answer. You must not assume that if two triangles look the same, they are congruent 10 cm 10 cm R Q 5 re these two triangles congruent? Justify your answer. 10 cm 10 cm 30 30 R Q 297
3 12.2 Recognising similar shapes 1 Which pairs of shapes are similar? Questions are targeted at the grades indicated D D Do not forget the corresponding angles must be equal. E F 60 G 45 H 60 60 45 2 The rectangles shown in the diagram are similar. 7.2 cm 23.04 cm 1.6 cm a cm alculate the value of the side a. Remember to check which sides are corresponding.... 3 re rectangles and similar? 4. 12 cm 2.3 cm 6.2 cm Explain your answer. 4 photograph is 12 cm long and wide. It is mounted on a piece of card so that there is a 4 cm border around the photograph. re the photograph and the card similar shapes? Explain your answer. 299
3 12.3 Similar triangles 1 Triangles and DEF are similar. a Write down three pairs of corresponding sides. b alculate the length x. x Questions are targeted at the grades indicated Write the equation with sides from DEF 40 y D 10 cm 80 7.5 cm E c alculate the length y. 60 3 cm 40 F * 2 a rove that triangle MN is similar to triangle. 6 cm b alculate the length. M 4. N 12 cm c alculate the length M. 4 cm S 3 cm T Q R Use the facts you know about parallel lines to prove corresponding angles are equal. 3 a rove that triangle QR is similar to triangle STR.... b alculate the length of SR.... 301
3 12.3 Similar triangles 4 a rove that triangle M is similar to triangle DM. * b alculate the length of side M. c alculate the length of side MD. Identify the corresponding sides before you begin. 3 cm 4.2 cm M 4.6 cm 1 D 5 a rove that triangle is similar to triangle DE. E has length 15 cm. 5 cm b alculate the length of side. c alculate the length of side E. D 7 cm E Identify the corresponding sides before you begin. 301
3 12.4 reas of similar shapes Questions are targeted at the grades indicated 1 entagons and are similar with scale factor 3. a alculate the area scale factor. length length gives area. The scale factor must be squared.... The area of is 9 cm 2. b alculate the area of....... 2 and Q are regular hexagons. a alculate the scale factor.... b alculate the area scale factor.... c The area of is 13.5 cm 2. alculate the area of Q. Q 3 cm 4.5 cm...... 3 rubber ball has a radius of 5 cm. The surface area of the ball is 314 cm 2. similar ball has a radius of. alculate the surface area of the larger ball. (Give your answer to the nearest cm 2.) 4 ylinders and Q are similar. The surface area of cylinder is 50 cm 2. The surface area of cylinder Q is 1800 cm 2. The radius of is 4 cm. alculate the radius of Q. 303
3 12.4 reas of similar shapes 5 These soup tins are similar. The area of the label for the large tin is 4 as big as the label for the small tin. How tall is the large tin? Use the area scale factor to find the scale factor.......... 7 cm Soup h Soup... 6 The leaves on a tree are similar. James measured the leaves as part of a science experiment. He estimated the area of the smaller leaf to be 20 cm 2 using a cm squared grid. 7 cm 12 cm Estimate the area of the larger leaf............. 7 Two cubes are dipped in gold. The smaller cube has length 2 cm and the larger cube has length 5 cm. How many times as much gold is needed for the larger cube? 303
3 12.5 Volumes of similar shapes Questions are targeted at the grades indicated 1 The diagram shows two bottles. The large bottle contains 250 cm 3. alculate the volume of the small bottle. length length length gives a volume. The scale factor must be cubed....... 12 cm 20 cm... 2 suitcase s height is 40 cm. similar suitcase from the same set has height 60 cm. If the small suitcase has volume 40 000 cm 3, find the volume of the larger suitcase. 3 The pentagonal prism has length 5 cm. Its volume is 50 cm 3. similar larger prism has length 7 cm. alculate the volume of the larger prism. 4 fish with a mass of 1.4 kg is 0.5 m long. alculate the expected mass of a similar fish whose length is 0.6 m. Work out the volume scale factor and use it to find the mass. 5 Two metal spheres have masses of 4 kg and 108 kg respectively. If the radius of the small sphere is 5 cm find the radius of the larger sphere. 305
3 12.5 Volumes of similar shapes 6 company sell bins for recycling. The bins are mathematically similar. 16-litre bin has height 30 cm. alculate the height of the 60-litre bin. 7 These funnels are mathematically similar. 6 cm The capacity of the larger funnel is 1350 ml and the capacity of the smaller funnel is 50 ml. The height of the smaller funnel is 6 cm. alculate the height of the larger funnel. 8 company provides gift boxes in three sizes. The boxes are geometrically similar. The height of the small box is 10 cm and the height of the medium box is 20 cm. The volume of the medium box is 2400 cm 3. a alculate the volume of the small box. b The large box has a volume of 64 800 cm 3. alculate the height of the large box. 305
3 12.6 Lengths, areas and volumes of similar shapes Questions are targeted at the grades indicated 1 Two similar cones have their surface areas in the ratio 9:16. Find the ratio of a the lengths...... b the volumes.... 2 Two solid spheres have surface areas of 2 and 72 cm 2 respectively. The mass of the smaller sphere is 2 kg. Find the mass of the larger sphere. Work out the volume scale factor and use it to find the mass............. 3 The volume of a prism is 120 cm 3. The volume of a larger prism is 405 cm 3. If the larger prism has a surface area of 315 cm 2, calculate the surface area of the smaller prism. 4 The areas of the bases of two glasses are in the ratio 4:9. a Find the ratio of their volumes. b If the smaller glass holds 124 cm 3 of liquid, how much will the large glass hold? 5 small bag that was carried as hand luggage has a length of 50 cm and a weight of 10 kg. similar bag of weight 18 kg is placed in the hold. alculate the length of this bag. 307
3 12.6 Lengths, areas and volumes of similar shapes 6 The ingredients of a bar of chocolate cost 25 p. giant sized bar is similar in shape, but five times longer than the original. alculate the cost of the ingredients of the giant sized bar. * 7 small cone is made by cutting the top from a large cone. The area of the base of the large cone is 100 cm 2. The area of the base of the smaller cone is 4 cm 2. The volume of the large cone is 750 cm 3. Find the volume of the smaller cone....... 8 The lid of a treasure chest has an area of 1800 cm 2. larger similar box has a lid of area of 11 250 cm 2. If the volume of the larger chest is 312 500 cm 3, find the volume of the smaller chest. 9 The surface area of a large sphere is 64 times the surface area of a smaller sphere. The volume of the small sphere is 50 cm 3. alculate the radius of the large sphere. The volume of a sphere is 4 3 πr 3. 307
3 12.6 Lengths, areas and volumes of similar shapes 10 Frustums and are similar. The volume of frustum is 162π cm 3. The volume of frustum is 384π cm 3. The surface area of is 28 2. alculate the surface area of frustum. * 307