1. Scale Factor of Similar Figures Finding the Scale Factor Finding Dimensions with Scale Factor Irma Crespo 2010

2. Warm Up What are the two things you need to show if a pair of polygons is similar? a)side lengths and angles are identical b)top and bottom are parallel c)corresponding angles are equal and the ratio of corresponding side lengths is the same d)corresponding angles are equal and the corresponding side lengths are the same

3. Your Scaled Measure If you are a quarter of your size. How tall and how wide are you going to be?

4. Scale Factor Scale factor is the ratio of the lengths of the corresponding sides of similar polygons. 3 LM ON 6 J G 2 I H 4 6464 = 3232 LO GI = NO JI = MN HJ = ML HG 6464 = 3232 = 3232 The Scale Factor

5. Find the Scale Factor Given that the rectangles are similar, what is the scale factor? 10 in 6 in 25 in 15 in a)1.5 b)2.5 c)5.5 d)19.5 HINT Pick a pair of corresponding side lengths.

6. Find the Scale Factor C A B D E 60.25 m 162 m 40 m 320 m Triangle ABD and triangle ACE are similar. a) b) c) d) 160 241 160 81 80 120 3232

7. Using Scale Factor Scale factor is used to enlarge or to reduce the size of an image of the original figure. A scale factor greater than 1 enlarges the size of an image of the original figure. A scale factor less than 1 reduces the size of an image of the original figure. A scale factor is multiplied to each corresponding side length of the original figure.

8. Scale Factor: Enlarge or Reduce? Scale Factor: ¾ Scale Factor: 5 Scale Factor:.99 Scale Factor: 1.98 Scale Factor: 2 Scale Factor: 8 / 3 reduce enlarge reduce enlarge

9. Finding Dimensions with Scale Factor Multiply the scale factor to each side length of the original figure.

10. Scale Factor Greater Than 1 The Scale Factor Multiply to each side length of the original figure. 3232 Given: J G 2 I H 4 original 3232 LM ON copy = 6262 = 6 3 2(2( 3232 )4(4( 3232 ) = 12 2 = 6 3

11. Scale Factor Less Than 1 The Scale Factor Given: 1919 = 5959 = 6969 = copy original 5 8 6 2323 5(5( 1919 ) = 6(6( 1919 )8(8( 1919 ) 8989 5959 2323 8989 1919 Multiply to each side length of the original figure.

12. Find the Dimension If a rectangle has a LENGTH of 6 cm and WIDTH of 2 cm, using a scale factor of 5, what would the new dimensions of the rectangle be? a)LENGTH = 11 cm; WIDTH = 7 cm b)LENGTH = 30 cm; WIDTH = 10 cm c)LENGTH = 10 cm; WIDTH = 6 cm d)LENGTH = 12 cm; WIDTH = 1 cm

13. Find the Dimension 18 8 108 With scale factor: 3, 4 what are the measurements of its similar polygon? a) b) c) d) 6 6 7.5 13.5 16 36 20 16 6 4.52 2 5 9 9 3

14. Take note of these… When finding the scale factor of similar polygons, compute for the ratio of corresponding side lengths. A scale factor greater than 1 enlarges the size of an image of the original figure. A scale factor less than 1 reduces the size of an image of the original figure. When finding dimensions of an image of the original figure, scale factor is multiplied to each corresponding side length of the original figure.

15. Exit Slip Make up a scale factor problem with your solution. You can either create a problem in finding the scale factor or finding dimensions. This is individual work and you get 2 extra credit points. Don’t forget to write your name and submit it before leaving class.

16. Practice Worksheet Complete the practice worksheet. Work with a partner or on your own. Submit completed worksheet for grading. Solutions are discussed the next day. Problem Solving Worksheet

17. Main Resources Math Connects: Concepts, Skills, and Problem Solving; Teacher Edition; Course 3, Volume 1 Columbus:McGraw-Hill, 2009. PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010.