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Symmetry and Similarity Review Short Answer 1. Determine the scale factor for this scale drawing. Original Scale diagram diagram 2. Determine the scale factor for this scale drawing. Original diagram Scale diagram 3. Which of trapezoids A, B, C, and D are scale diagrams of trapezoid O? O A B C D 4. A square has side length 4.3 cm. The square is enlarged by a scale factor of 3.4. Determine the side length of the enlargement. 5. A circle has diameter 48 cm. The diameter of the reduction is 42 cm. Determine the scale factor of the reduction as a fraction and as a decimal. . 6. Determine the scale factor for each reduction. a) Quadrilateral B is a reduction of quadrilateral A. b) Quadrilateral C is a reduction of quadrilateral A. c) Quadrilateral B is a reduction of quadrilateral C. B A C 7. Determine the value of y in this proportion: 8. These quadrilaterals are similar. Determine the value of x. 21 cm 14 cm x 42 cm 9. These quadrilaterals are similar. Determine the values of x and y°. 13.6 31° 10.2 15.3 x y° 10. Quadrilateral PQRS is similar to quadrilateral ABCD. If AB = 3 cm, BC = 4 cm, and QR = 8.96 cm, determine the length of PQ. 11. Determine the length of EF in these similar triangles. A D 9 C B 16.2 18 F E 12. Determine the length of BD in these similar triangles. A B C 20 7 D 10.5 E 13. Determine the length of RS in these similar triangles. P 14 m Q 159.6 m R T 19 m S 14. Determine the length of NO in these similar triangles. N L 3.9 cm P 4.8 cm M 12.8 cm O 15. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by drawing its other half. y 6 5 4 3 2 1 1 2 3 4 5 6 7 x 16. Identify the pentagons that are related to the black pentagon by a line of reflection. Describe the position of each line of symmetry. y 11 10 9 R 8 7 6 5 4 P S 3 2 Q 1 1 2 3 4 5 6 7 8 9 10 11 12 13 x 17. Draw the rotation image after rotating the shape 90° clockwise about P. P 18. What is the order of rotational symmetry and angle of rotation symmetry for this design? 19. Describe the rotational symmetry and line symmetry of this design. 20. Which of triangles A, B, and C are related to the shaded triangle by rotational symmetry about the origin? y 5 4 3 B 2 1 –5 –4 –3 –2 –1 –1 C –2 1 2 3 4 5 x A –3 –4 –5 21. Determine whether polygon A and its image are related by line symmetry after each transformation: i) a translation R3 ii) a translation U6 iii) a reflection in a vertical line through 4 in the x-axis iv) a reflection in a horizontal line through 7 in the y-axis y 13 12 11 10 9 8 7 6 5 4 3 A 2 1 1 2 3 4 5 6 7 8 x Problem 22. Determine each scale factor. a) Square TPQR is a scale drawing of square TABC. b) Square TGHK is a scale drawing of square TDEF. c) Square TPQR is a scale drawing of square TDEF. d) Square TLMN is a scale drawing of square TABC. Q P M L H G E D A T B C F K N R 23. Calculate the values of the variables in this proportion: 24. This polygon is part of a larger shape. Draw the image of the polygon after each reflection: i) a reflection in the y-axis ii) a reflection in the x-axis iii) a reflection in the oblique line through (–5, 5) and (5, –5) How many lines of symmetry does the shape have? y 5 4 3 2 1 –6 –5 –4 –3 –2 –1 –1 –2 –3 –4 –5 1 2 3 4 5 6 x Symmetry and Similarity Review Answer Section SHORT ANSWER 1. ANS: The scale factor is 2. PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 2. ANS: The scale factor is 3.5. PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 3. ANS: Trapezoids C and D PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 4. ANS: 14.62 cm PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 5. ANS: PTS: 1 DIF: Easy REF: 7.2 Scale Diagrams and Reductions LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 6. ANS: a) b) c) PTS: 1 DIF: Moderate REF: 7.2 Scale Diagrams and Reductions LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 7. ANS: 0.45 PTS: 1 DIF: Easy REF: 7.3 Similar Polygons LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 8. ANS: x = 28 cm PTS: 1 DIF: Easy REF: 7.3 Similar Polygons LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 9. ANS: x = 20.4 y° = 31° PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Conceptual Understanding | Procedural Knowledge 10. ANS: PQ = 6.72 cm PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 11. ANS: EF = 32.4 PTS: 1 DIF: Easy REF: 7.4 Similar Triangles LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 12. ANS: BD = 8 PTS: 1 DIF: Moderate REF: 7.4 Similar Triangles LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 13. ANS: RS = 117.6 m PTS: 1 DIF: Moderate REF: 7.4 Similar Triangles LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 14. ANS: 10.4 cm PTS: 1 DIF: Moderate REF: 7.4 Similar Triangles LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 15. ANS: y 6 5 4 3 2 1 1 2 3 4 5 6 7 x PTS: 1 DIF: Easy REF: 7.5 Reflections and Line Symmetry LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 16. ANS: Pentagon P is the reflection image of the black pentagon in the vertical line through 3 on the x-axis. Pentagon Q is the reflection image of the black pentagon in the horizontal line through 3 on the y-axis. Pentagon R is the reflection image of the black pentagon in the oblique line through (4, 10) and (12, 2). Pentagon S is the reflection image of the black pentagon in the vertical line through 7.5 on the x-axis. PTS: 1 DIF: Moderate REF: 7.5 Reflections and Line Symmetry LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Conceptual Understanding | Communication 17. ANS: P PTS: 1 DIF: Easy REF: 7.6 Rotations and Rotational Symmetry LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 18. ANS: 4; 90° PTS: 1 DIF: Moderate REF: 7.6 Rotations and Rotational Symmetry LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 19. ANS: Rotational symmetry of order 4 about the centre 4 lines of symmetry through the centre PTS: 1 DIF: Easy REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 20. ANS: Triangles A and B PTS: 1 DIF: Moderate REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 21. ANS: i) There is no line of symmetry. ii) The line of symmetry is the horizontal line through 6 on the y-axis. iii) The line of symmetry is the vertical line through 4 on the x-axis. iv) The line of symmetry is the horizontal line through 7 on the y-axis. PTS: 1 DIF: Moderate REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge | Communication PROBLEM 22. ANS: a) The scale factor is: b) The scale factor is: c) The scale factor is: d) The scale factor is: PTS: 1 DIF: Moderate REF: 7.1 Scale Diagrams and Enlargements LOC: 9.SS4 TOP: Shape and Space (Transformations) KEY: Procedural Knowledge 23. ANS: PTS: 1 DIF: Moderate REF: 7.3 Similar Polygons LOC: 9.SS3 TOP: Shape and Space (3-D Objects and 2-D Shapes) KEY: Procedural Knowledge 24. ANS: 6 y 5 4 3 2 1 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 x –2 –3 –4 –5 –6 The shape has four lines of symmetry. PTS: 1 DIF: Moderate REF: 7.5 Reflections and Line Symmetry LOC: 9.SS5 TOP: Shape and Space (Transformations) KEY: Problem-Solving Skills | Procedural Knowledge