Worksheets for GCSE Mathematics Similar & Congruent Shapes Mr Black's Maths Resources for Teachers GCSE 1-9 Shape
Similarity & Congruence Worksheets Contents Differentiated Independent Learning Worksheets Congruent Shapes Page 2 Similar Lengths Page 3 Similar Areas Page 4 Similar Volumes Page 5 Similar Shapes Page 6 Solutions Congruent Shapes Page 7 Similar Lengths Page 8 Similar Areas Page 8 Similar Volumes Page 9 Similar Shapes Page 9 1
Congruence Q1. Which shape from each set is the odd one out? c) d) Q2. State whether each of pair of triangles a to d is congruent. Explain your reasoning. c) d) Q3. ABC is an isosceles triangle with AB = CB. Show that ABD is congruent to CBD Q4. Explain why these two trapezia may not be congruent. 2
Similar Lengths Q1. The two triangles below are similar. What is: The ratio BC : EF? The length scale factor? c) The angle DEF? d) The length DE? e) The length AC? Q2. The two quadrilaterals are similar. Calculate the length scale factor. Calculate the length of c. c) Calculate the length of d. Q3. Calculate the unknown length for each of these similar shapes. Q4. Calculate the length of y. 3
Area of Similar Shapes Q1. These two shapes are similar. c) d) Calculate the length scale factor. Calculate the area scale factor. Calculate the length a. Calculate the area of the larger shape. Q2. c) These two shapes are similar. Calculate the length scale factor. Calculate the area scale factor. Calculate the area of the larger shape. Q3. A medium size photograph is 16 cm long, 8 cm wide and has an area of 128cm 2. A small size photograph is 8 cm long. What is the width of the small size photograph? What is the area of the small size photograph? Q4. A box of height 6 cm has a surface area of 240 cm 2. What is the surface area of a similar box three times as high? Q5. These pentagons are regular. G has an area of 50 cm 2. H has an area of 450 cm 2 What is the length of the base of H? Q6. Three similar arrows are shown. C is 2.5 times the size of B. B has an area of 24 cm 2. Calculate the length of edge C. Calculate the area of shape C c) Calculate the area of shape A. A B C 6cm Area = 192 cm 2 24 cm c 4
Volume of Similar Shapes Q1. c) Box A is similar to box B. Box A has a length of 4 cm and a volume of 12 cm 3. Box B has a length of 8 cm. Calculate the length scale factor. Calculate the volume scale factor. Calculate the volume of box B. Volume - 12 cm 3 B A 4 cm 8 cm Q2. c) These two cans are similar in shape. Jar G has a diameter of 6 cm and a volume of 250ml. Jar H has a diameter of 18 cm. Jar H Jar G Calculate the length scale factor. Calculate the volume scale factor. Calculate the capacity of Jar H. 250 ml 6 cm 18 cm Q3. Two spheres, one of radius 5 cm and the other of radius 20 cm are filled with gas. How many times as much gas is needed for the larger sphere? Q4. These two solids are similar in shape. Solid X has a hollow semi-circle of diameter 9 cm and a weight of 250 g. Solid Y has a weight of 6750 g. T cm Calculate length T. Q5. A bottle has a volume of 500 ml. A simlilar bottle is double the height. What is the volume of the larger bottle? Q6. The volumes of two similar figures are 62 cm 3 and 125 cm 3. The height of the smaller figure is 6 cm. Calculate the height of the larger figure. Q7. The main triangular prism has a volume of 7812.5 cm 3. The grey trianglular prism has a volume of 500 cm 3. Calculate the length of k. 5
Similar Shapes Q1. Complete the table. Length Scale Length Ratio Area Scale Area Ratio Volume Scale Volume Ratio 2 1 : 2 1 : 4 8 1 :4 216 1 9 8: 125 Q2. Two cuboids, A and B, are mathematically similar. The length of cuboid A is 3 cm and cuboid B 9 cm. The surface area of shape A is 40 cm 2. Calculate the surface area of shape B. The volume of shape B is 567 cm 3. Calculate the volume of shape A. A B 3 cm 9 cm Q3. Two containers are mathematically similar and have masses of 32 kg and 108 kg. The area of the label on the small cylinder is 12 cm 2. Calculate the area of the label on the large cylinder. Q4. 8 m 2 of fabric is required to cover a small chair. What area of fabric is required to cover a chair 1.5 times larger? Q5. Two solids, X and Y, are mathematically similar. The total surface area of solid X is 24 cm 2. The total surface area of solid Y is 216 cm 2. The height of solid X is 2.5 cm. Calculate the height of solid Y. The volume of solid Y is 1404 cm 3. Calculate the volume of solid X. Q6. A rubber ball has a diameter of 5.6 cm and volume of 735.62 cm 3. It is decided to increase the diameter by 20%. Calculate the new volume of the ball. 5.6 cm 6
Congruence Solutions Q1. Which shape from each set is the odd one out? c) d) Q2. Congruent (SSS) Congruent (SAS) c) Congruent (ASA) d) Congruent (SAS) Q3. AB = BC, BD = BD. ADB = BDC. Therefore SAS Q4. Lengths could be enlarged so angles would remain the same. 7
Solutions Similar Lengths Q1. 1 : 2 2 c) 40 d) 10 cm e) 4 cm Q2. 3 6 cm c) 3 cm Q3. e = 15 units f = 20 units c) g = 12 units, h = 26.25 units Q4. y = 20 cm Area of Similar Shapes Q1. 2 4 c) 4 d) 40 cm 2 Q2. 3 9 c) 108 cm 2 Q3. 4 cm 32 cm 2 Q4. 2160 cm 2 Q5. 18cm Q6. 60 cm 2 12 cm 2 c) 1200 cm 2 8
Volume of Similar Shapes Q1. 2 8 c) 96 cm 3 Q2. 3 27 c) 6750 ml Q3. 64 times more gas is needed to fill the larger sphere. Q4. T = 27 cm Q5. 4 Litres Q6. 9 cm Q7. k = 6 Similar Shapes Q1. Length Scale Length Ratio Area Scale Area Ratio Volume Scale Volume Ratio 2 1 : 2 4 1 : 4 8 1 : 8 4 1 :4 16 1 : 16 64 1 : 64 6 1 : 6 36 1 : 36 216 1 : 216 1 3 3 : 1 1 9 9 : 1 1 27 27 : 1 2.5 2 : 5 6.25 4 : 25 15.625 8: 125 Q2. 360 cm 2 21 cm 3 Q3. 27 cm 2. Q4. 18 m 2 Q5. 7.5 cm 52 cm 3 Q6. 1271.2 cm 3 9