Math 9 - Similar and Transformations Unit Assignment
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1 Math 9 - Similar and Transformations Unit Assignment Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the scale factor for this scale diagram. Original diagram Scale diagram a. 32 b. 8 c. 4 d A rectangle has length 6 cm and width 4 cm. The rectangle is to be enlarged by a scale factor of 8. Calculate the length of the enlargement. a. 80 cm b. 48 cm c. 32 cm d. 14 cm 3. A pencil has diameter 9 mm. A scale diagram of the pencil has diameter 4.5 cm. Determine the scale factor of the diagram. a. 50 b. 0.5 c. 1 d A circle has diameter 56 cm. The diameter of the reduction is 7 cm. Determine the scale factor. a. b. 8 c. d. 49
2 5. Determine the scale factor for this reduction. Reduction Original a. 8 b. 4 c. 1 d Which of triangles, Q, R, and S are reductions of triangle X? X Q R S a. Triangles, Q, and S c. Triangles and Q b. Triangles Q and S d. Triangles, Q, and R 7. Calculate the side length, in units, in this proportion: a b c. 4 d Identify similar quadrilaterals. Q R S a. and Q b. and R c. R and S d. Q and S
3 9. Which triangle is similar to ABC? 5 A Q N 9 6 L D Z 4 7 M X Y B 11 C R E 10 F a. XYZ b. QR c. LMN d. DEF 10. Determine the length of AE in this pair of similar triangles. A B 3 E 10 D 4 C a. 3.3 b c. 7.5 d Determine the measure of KML in this pair of similar triangles. o o Q R M L K a. 55 b. 104 c. 41 d. 35
4 12. Which shapes have at least 2 lines of symmetry? Q R S a. Shapes, Q, S c. Shapes Q, R, S b. Shapes, S d. Shapes, Q, R, S 13. Identify the triangles that are related to the black triangle by a line of reflection. 7 y Q R S x a. Triangles, Q, R, S c. Triangles R, S b. Triangles Q, R d. Triangles Q, R, S 14. What is the angle of rotation symmetry for a shape that has rotational symmetry of order 5? a. 144 b. 36 c. 72 d What is the order of rotational symmetry and angle of rotation symmetry for this regular pentagon? a. 5; 75 b. 6; 120 c. 5; 72 d. 5; Which figure shows the rotation image of circle A after a 135 counterclockwise rotation about its centre? Circle A Figure i Figure ii Figure iii Figure iv a. Figure iv b. Figure i c. Figure iii d. Figure ii
5 17. Describe the rotational symmetry and line symmetry of this parallelogram. a. Rotational symmetry of order 2 about the centre; no line symmetry b. Rotational symmetry of order 2 about the centre; 1 line of symmetry through the centre c. Rotational symmetry of order 1 about the centre; 1 line of symmetry through the centre d. No rotational symmetry; no line symmetry 18. Which of the following letters have both rotational symmetry and line symmetry? a. H, O, X b. K, H, X c. N, H, X d. S, H, O, X 19. Which figure is not related to the shaded shape by rotational symmetry about point? y 5 4 Figure i Figure ii Figure iii Figure iv x a. Figure ii b. Figure iv c. Figure ii d. Figure iii Numerical Response 1. Determine the scale factor for this scale drawing. Original diagram Scale diagram
6 2. Rectangle ABCD is similar to rectangle QRS. If AB = 7.2 cm, BC = 5.7 cm, and Q = 4.8 cm, determine the length of QR. 3. This scale diagram shows the measurements a surveyor made to determine the height of a building. What is this height? Building 33 m 56 m 24 m Long Answer Section 1. Which pentagon is similar to the shaded pentagon? Show your work.
7 2. These two quadrilaterals are similar. Calculate the length of: a) N b) TS 3. To determine the distance, d, across a pond, Ari uses this diagram. What is the distance across the pond? 4. Which of the following traffic signs have a line of symmetry? How many lines of symmetry in each case? Draw in the lines of symmetry. a) b) # lines of symmetry: # lines of symmetry: c) d) # lines of symmetry: # lines of symmetry:
8 5. What is the order and angle of rotational symmetry for each shape? a) b) c) d) 6. Describe the rotational symmetry and line symmetry of each wheel cover: sketch the lines of reflection mark the centre of rotation state the order and angle of rotation a) b) # lines of symmetry: # lines of symmetry:
9 c) d) # lines of symmetry: # lines of symmetry: 7. Look at the squares below. Which of the squares, A, B, C and D are related to the dark square: a) by rotational symmetry about the origin? b) by line symmetry?
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