- Chapter 4: "Scale Factors and Similarity" -

Transcription

1 Mathematics 9 C H A P T E R Q U I Z Form P - Chapter 4: "Scale Factors and Similarity" - Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A scale of 4:9 means a. there are 9 units of the image for every 4 units of actual size b. there are 9 units of the image for every unit of actual size c. there are 4 units of the image for every unit of actual size d. there are 4 units of the image for every 9 units of actual size 2. Compare Figure B to Figure A. Figure B is a. a reduction of Figure A c. a proportion of Figure A b. an enlargement of Figure A d. a scale factor of Figure A

2 3. In the drawings shown, the scale factor used to create Figure A from Figure B is a. 2 c. 4 b. 3 d Compare the letter on the right to the letter on the left. The letter on the right a. has a scale factor equal to 1 c. has a scale factor less than 1 b. has a scale factor greater than 1 d. has no scale factor Page 2 of 15

3 5. The letter on the right is drawn from the letter on the left using a scale factor. The scale factor is a c b d A scale diagram of two flower pots is shown below. If the flower pot on the left has a base with a diameter of 9 cm, what is the approximate diameter of the base of the flower pot on the right? a. 7.0 cm c. 6.0 cm b cm d. 9.7 cm Page 3 of 15

4 7. A digital picture on a computer screen is 8.2 mm wide. When the picture is printed, the image enlarged by a scale of 1:2.1. What is the width of the printed picture? a. 6.1 mm c mm b mm d mm 8. What scale is used to create the image on the right from the original image on the left? a. 1:2 c. 2:1 b. 1:4 d. 4:1 9. The scale diagram below shows a cross-section of a pipe. The scale used to create the diagram is 1:3. What is the inside diameter of the actual pipe? a. 4.0 cm c. 0.9cm b. 6.0 cm d. 1.8 cm Page 4 of 15

5 10. In the two triangles shown, A and D are a. complimentary angles c. exterior angles b. corresponding angles d. inscribed angles 11. ABC and EFG are a. similar triangles c. proportional triangles b. corresponding triangles d. equal triangles Page 5 of 15

6 12. What is the measure of angles K and S? a. 30 c. 80 b. 60 d. 90 Page 6 of 15

7 13. The two triangles shown are a. complimentary triangles c. equal triangles b. equilateral triangles d. similar triangles Page 7 of 15

8 14. What scale must be applied to make JKL from RST? a. 1:5 c. 2:1 b. 1:4 d. 4:1 Page 8 of 15

9 15. Triangle B is drawn from Triangle A using a scale of 2:1. If the hypotenuse of Triangle A is 35 mm, what is the length of the hypotenuse of Triangle B? a. 37 mm c. 70 mm b. 33 mm d. 72 mm Page 9 of 15

10 16. Triangles A and B are similar isosceles triangles, related by a scale of 1:2. If each leg of Triangle A measures 20 cm, calculate the approximate length of the hypotenuse of Triangle B. a cm c cm b cm d cm 17. A scale diagram of a field uses a scale of 2 mm:1 m. Determine the actual distance from A to C. a. 92 m c. 88 m b. 45 m d. 180 m Page 10 of 15

11 18. Kendra wants to draw a scale diagram of the field shown in the sketch. She plans to use a scale of 8 mm:1 m. How long should she draw line AB if she wants to represent a distance of 184 m? a. 25 mm c. 23 mm b. 21 mm d mm 19. A farmer sketched the following layout of a field. He wants to develop a scale drawing of the field in which 1 cm on the diagram represents 20 m of actual distance. The pipeline runs across the diagonal of the field. Approximately how long will the line that represents the pipeline be in the scale diagram? a cm c. 6.4 cm b cm d. 9.4 cm 20. ΔABC is a scalene triangle. A similar triangle, ΔDEF, is developed using a scale factor of 3. In ΔDEF, DEF is a. equal to ABC c. equal to three times ABC b. equal to one-third ABC d. equal to two times ABC Page 11 of 15

12 21. ΔABC is a scalene triangle, with ABC equal to 86. A similar triangle, ΔDEF, is made using a scale factor of 3. In ΔDEF, DEF is a. 45 c. 49 b. 129 d How many similar triangles are there in the regular polygone shown? a. 0 c. 4 b. 2 d This polygon has sides that are 2.0 cm each. If a similar polygon was created using a scale factor of 9.0, determine the side length of the similar polygon. a cm c cm b cm d cm Page 12 of 15

13 24. Compare hexagon A to hexagon B. Hexagon A has a. angles that are smaller than the angles in hexagon B b. angles that are proportional to the angles in hexagon B c. angles that are larger than the angles in hexagon B d. angles that are equal to the angles in hexagon B Short Answer 25. The scale diagram of a playground uses a scale of 1:477. The length of the court measures 15 cm in the diagram. What is the actual length of the playground, in metres? 26. Richelle designed a tote bag. In the design, the length of the bag is 10 cm. The actual length of the bag is 24 cm. What scale factor did Richelle use in her design? 27. You want to draw a triangle similar to the one shown. You are going to use a scale factor of 2. What should the length of the sides of the new triangle be? Page 13 of 15

14 Problem Write your answer in the space provided. 28. Use the grid provided to create a drawing of the letter below using a scale factor of State whether your drawing is an enlargement or a reduction. Page 14 of 15

15 29. A map of a nature reserve shows the location of three look-out points. On the map, the distance between Point A and Point B is 5.1 cm and the distance between Point B and Point C is 6.4 cm. Each centimetre on the map represents 30 km of actual distance. Calculate the actual distance between Point A and Point C. 30. An observer stands 18.2 m from the door of a house, and 2.6 m from the street. The observer is 1.3 m tall. Calculate the height of the house. Page 15 of 15