Similarity and Transformation
How to figure out is figures are similar?
Figures are similar if the second can be obtained from the first by a sequence transformations .To find if two figures are similar you must write ratios to compare the lengths of the side. If the ratios for the ALL the sides are not the same than the figures are not similar. Ex. AB/CD = 3/4; EF/GH = 3/4; IJ/KL = 3/4 are similar figure but AB/CD=3/4; EF/GH = 2/5; IJ/KL = 3/4 are not.
When you have two similar figures one of them will be dilated. Dilation is transformation that enlarges or reduces a figure by a scale factor. A scale factor is the ratio of the lengths of two corresponding sides of two similar polygons. To use transformations when finding similarity use scale factor.
Ex. Ben enlarges photo as shown by a scale factor of 4 for his webpage. He then enlarges the webpage photo .5 to print for his computer science teacher. If the original photo is 1 in by 2 inches, what are the dimensions of the print? Are the manipulated photos similar to originals?
Multiply for the webpage size.
1× 4 = 2 in 2× 4 = 8 in
Now multiply 2 in by 8 in by .5 to get the print size.
2 in × .5 = 1 in 8 in × .5 = 4 in
The webpage is 2 in by 8 in and the print is 1 in by 4 in. All three photos are similar since each enlargement is a result of dilation.