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Understanding Similar Figures: Stretching and Shrinking Concepts

Dive into the fundamentals of similar figures with this comprehensive review. Explore key concepts such as scale factors, equivalent ratios, and the properties of similar polygons through engaging vocabulary activities and investigations. Learn how dimensions change when shapes are enlarged or reduced, and grasp how side lengths and angles relate between similar figures. This unit test review is perfect for reinforcing your understanding of similarity, ratios, and geometric transformations, ensuring you're well-prepared for any assessment on this topic.

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Understanding Similar Figures: Stretching and Shrinking Concepts

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  1. What do you know? Stretching and Shrinking SIMILAR FIGURES Unit Test Review

  2. What Do You Know? Enlarging & Reducing Shapes Similar Figures Similar Polygons Similarity & Ratios Vocabulary 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

  3. Vocabulary - 100 Define Similar Check Your Answer

  4. Vocabulary - 100 Same shape, but not the same size. Back to Game Board

  5. Vocabulary - 200 Draw 2 figures and color code their corresponding sides Check Your Answer

  6. Vocabulary - 200 The side in the same relative position on a similar figure. Back to Game Board

  7. Vocabulary - 300 Define Scale Factor Check Your Answer

  8. Vocabulary - 300 The number used to multiply the lengths of a figure to stretch or shrink it to a similar image. Back to Game Board

  9. Vocabulary - 400 Give an example of equivalent ratios. Check Your Answer

  10. Vocabulary - 400 Ratios whose fraction representation are the same. Back to Game Board

  11. Vocabulary - 500 Draw 2 rectangles and color code the adjacent sides. Check Your Answer

  12. Vocabulary - 500 Adjacent is the sides that are touching. Back to Game Board

  13. Investigation 1 - 100 What is 10% of 80? Check Your Answer

  14. Inv. 1 Answer - 100 10% of 80 = 8 Back to Game Board

  15. Investigation 1 - 200 If a three-band stretcher is used to enlarge a rectangle, how will the perimeter of the enlargement compare to the perimeter of the original? Check Your Answer

  16. Inv. 1 Answer - 200 The perimeter of the enlargement will be three times larger than the original. Back to Game Board

  17. Investigation 1 - 300 If a three-band stretcher is used to enlarge a triangle, how will the angles of the enlargement compare to the angles of the original? Check Your Answer

  18. Inv. 1 Answer - 300 Corresponding angles of similar figures have the same measure. Back to Game Board

  19. Investigation 1 - 400 Check Your Answer

  20. Inv. 1 Answer - 400 Back to Game Board

  21. Investigation 1 - 500 If a three-band stretcher is used to enlarge a triangle, how will the area of the enlargement compare to the area of the original? Check Your Answer

  22. Inv. 1 Answer - 500 The area of the enlargement will be 9 times larger. Back to Game Board

  23. Investigation 2 - 100 Suppose you used the rule (6x, 6y) to transform a figure into a new figure. How would the angles of the new figure compare with the angles of the original? Explain. Check Your Answer

  24. Inv. 2 Answer - 100 The angles would be the same because 6 is being multiplied by the length and width. The two figures will be similar which makes their corresponding angles the same! Back to Game Board

  25. Investigation 2 - 200 Write a rule that can be applied to the length and width of a rectangle to create a figure that is not similar. Check Your Answer

  26. Inv. 2 Answer - 200 Answers may vary. Back to Game Board

  27. Investigation 2 - 300 If you enlarge the rectangle below at a scale factor of 200%, what will the new dimensions be? 4 cm 10 cm Check Your Answer

  28. Inv. 2 Answer - 300 8 cm 20 cm • Steps: • Convert 200% to decimal of 2.00 • 2 x 10 = 20 cm • 2 x 4 = 8 cm Back to Game Board

  29. Investigation 2 - 400 Robert graphed a triangle on a coordinate plane. He decided to see what happened if he transformed the shape with the rule (2x, y+1). Which of the following tables could be an actual representation of his original triangle and his transformation? Explain. A B Check Your Answer

  30. Inv. 2 Answer - 400 B. Back to Game Board

  31. Investigation 2 - 500 • Tim wants to create Dug, a friend to Mug on the coordinate plane. His rule for Dug in relation to Mug is (x+1, y+2). Which of the following statements best describes Dug? • Dug will be enlarged so he is 2 times as large as Mug. • Dug will not be similar to Mug. • Dug will be congruent to Mug, but moved 1 space to the right and 2 spaces above Mug. Check Your Answer

  32. Inv. 2 Answer - 500 • Dug will be congruent to Mug, but moved 1 space to the right and 2 spaces above Mug. • (x+1, y+2) does not change the size at all. Adding a number to x and y just moves the figure in the coordinate plane. Back to Game Board

  33. Investigation 3 - 100 The quadrilaterals below are similar. What is the scale factor from the small quadrilateral to the large quadrilateral? Check Your Answer

  34. Inv. 3 Answer - 100 The scale factor is 5. Back to Game Board

  35. Investigation 3 - 200 ABCD is similar to EFGH. What is the scale factor from rectangle ABCD to rectangle EFHG? F E A B 3 cm 6 cm D C G H 9 cm Check Your Answer

  36. Inv. 3 Answer - 200 The scale factor is 2. 6/3 = 2 F E A B 3 cm 6 cm D C G H 9 cm Back to Game Board

  37. Investigation 3 - 300 ABCD is similar to EFGH. What is the scale factor from rectangle EFHG to rectangle ABCD? F E A B 3 cm 6 cm D C G H 9 cm Check Your Answer

  38. Inv. 3 Answer - 300 The scale factor is ½. 3/6 = ½ . ½ is the reciprocal of 2/1. F E A B 3 cm 6 cm D C G H 9 cm Back to Game Board

  39. Investigation 3 - 400 What is the measure of angle T? 50° T Check Your Answer

  40. Inv. 3 Answer - 400 T = 40° 90° + 50° = 140° 180° – 140° = 40° 50° T Back to Game Board

  41. Investigation 3 - 500 ABCD is similar to EFGH. How does the area of ABCD compare to EFGH? Explain. F E A B 3 cm 6 cm D C G H 9 cm Check Your Answer

  42. Inv. 3 Answer – 500 The area is 4 times larger because it is the (scale factor)2 22 = 4 F E A B 3 cm 6 cm D C G H 9 cm Back to Game Board

  43. Investigation 4 - 100 Check Your Answer

  44. Inv. 4 Answer - 100 Back to Game Board

  45. Investigation 4 - 200 Check Your Answer

  46. Inv. 4 Answer - 200 Back to Game Board

  47. Investigation 4 - 300 Back to Game Board

  48. Inv. 4 Answer - 300 Back to Game Board

  49. Investigation 4 - 400 Back to Game Board

  50. Inv. 4 Answer - 400 Back to Game Board

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